Download The Relationship between Age Structure and

Journal of
10.1177/0022427806286565
Phillips
/ U.S.
Research
Age Structure
in Crimeand
andHomicide
Delinquency
Rates
The Relationship between
Age Structure and
Homicide Rates in the
United States, 1970 to 1999
Journal of Research in Crime
and Delinquency
Volume 43 Number 3
August 2006 230-260
© 2006 Sage Publications
10.1177/0022427806286565
http://jrc.sagepub.com
hosted at
http://online.sagepub.com
Julie A. Phillips
Rutgers University
The nature of the temporal association between age structure and homicide
rates between 1970 and 1999 is examined using U.S. county data. Specifically,
the following questions are asked: (a) does the strong temporal association
between the relative size of the young population and homicide rates demonstrated at the U.S. national level hold at a disaggregated level and (b) does the
association between the proportion young and homicide rates differ by varying
social and economic conditions. The results confirm that a positive temporal
association between age composition and homicide rates exists within U.S.
counties. However, the analysis reveals that other criminogenic forces, such as
poor social conditions that produce higher crime rates, can alter the association
between the relative size of the young population and homicide rates. The positive effect of the percentage aged 15 to 24 years on homicide rates is generally
attenuated when criminogenic conditions exist while that of the percentage
aged 25 to 34 years tends to be accentuated under such circumstances.
Keywords: age composition; homicide; time series; United States
A
lthough criminologists continue to debate the relative importance of
many social, economic, and cultural factors that may explain involvement in crime, there traditionally has been consensus about one variable and
its relationship to crime: age. Criminologists have long recognized that
young people are disproportionately involved in crime, with criminal activity
increasing dramatically during the teen years, peaking at around age 20, and
Author’s Note: This research was supported in part by a grant from the National Science Foundation (SES #0111542). I thank David Greenberg, Ken Land, Paul Allison, Rosemary Gartner,
Michael Phillips, and Sarah Rosenfield for helpful comments. Xiaohui Xin and Ji Woong Bo provided excellent research assistance. Please send all correspondence to Julie Phillips, Department
of Sociology, 54 Joyce Kilmer Avenue, Piscataway, NJ 08854-8045; jphillips@sociology
.rutgers.edu. (T) 732-932-1824 (F) 732-445-0974.
230
Phillips / U.S. Age Structure and Homicide Rates 231
then steadily declining over the rest of the life course, with very low levels
observed after age 65. It follows from this premise that increases and
decreases in the young population produce corresponding rises and falls in
crime levels over time and place. Indeed, criminologists largely rely on standard demographic indicators, such as birth, death, and immigration rates, as a
mechanism for forecasting a population’s future age structure and, in turn,
future crime trends.
The empirical evidence concerning the temporal association between age
structure and crime levels in the United States certainly provides support for
this approach to forecasting crime. For example, several studies using demographic techniques estimated that as much as half of the increase in crime
rates during the 1960s can be accounted for by shifts in the population’s age
composition toward greater percentages in the younger age groups
(Ferdinand 1970; Sagi and Wellford 1968). Steffensmeier and Harer (1987)
confirmed that the subsequent drop in the crude index rate between 1980 and
1984 can be partially explained by the aging of the U.S. population during
that time period as the baby boomers began to move out of the crime-prone
age groups. Cohen and Land (1987) further demonstrated that the relationship between age structure and crime is symmetric, with the 1980s declines
in crime rates as great as the increases observed during the 1960s and 1970s.
Several cross-national studies, however, raise questions about the supposedly ubiquitous temporal association between a population’s age composition and homicide rates. Based on a sample of 18 developed countries, Gartner (1990) found no significant association between the relative size of the
young population and homicide rates. Gartner and Parker (1990), in their
analysis of five developed countries over a 70-year period, demonstrated that
changes in the proportion of young males in a population do not have consistent effects on homicide rates across time and place. A strong effect of age
composition on time trends in homicide levels was observed in only two of
the five countries they analyzed, namely the United States and Italy. A subsequent study by Pampel and Gartner (1995) compared 18 countries over a 36year period and revealed that national context, namely the relative development of national institutions for collective social protection, mitigates the
otherwise positive association between age structure and homicide levels.
Moreover, Marvell and Moody’s (1991) comprehensive review of 90 studies
examining the age-crime relationship noted that only a limited number
reported significant associations.
This empirical evidence suggests that the common wisdom of a universal
relationship between age structure and crime is overly simplistic—that, in
fact, the association may vary under different social and cultural conditions—and raises important questions about the age composition-crime rela-
232 Journal of Research in Crime and Delinquency
tionship in the United States. The majority of studies demonstrating the
strong temporal association between age structure and crime rates are based
on U.S. national data and essentially estimate an average effect of age structure on crime in the United States, a country with distinctive regional cultures
and composed of heterogeneous populations. Whether the strong temporal
relationship observed at the national level between age structure and homicide rates holds across places within the United States is less well documented, although several studies conducted at the state, city, and county levels that include age structure as a control variable indicate that increases in
the proportion young are positively associated with overall crime rates over
time (Lott 1998; Marvell and Moody 1996). In addition, very little research
to date attempts to identify possible sources of variation in the sensitivity of
homicide rates to changes in age composition. This omission is surprising,
given cross-national evidence suggesting that the sensitivity of crime levels
to changes in age structures may vary under different social conditions, and
theoretical arguments that claim to explain why involvement in crime varies
with age.
In this article, cross-sectional (county level) and time series data from the
United States are combined to answer two research questions. First, I ask
whether a strong temporal relationship between age structure and crime
exists at a more disaggregated level within the United States. By pooling
information on multiple counties and years, I address not only this substantive question, but also make a methodological contribution to the literature
(see Levitt [2001] for more detailed discussion). The longitudinal relationship between age structure and homicide rates is estimated using several hundred replications of the time-series and thus provides a far stronger basis for
generalization about the temporal relationship between age structure and
homicide rates in the United States. Furthermore, the pooled time-series
analysis offers a more rigorous test of the correlates associated with homicide by controlling for stable unmeasured characteristics of counties and
period (Johnston and DiNardo 1997).
Second, I determine whether and how the association between age composition and homicide may be affected by varying social and economic conditions. Specifically, I examine how factors that differ across counties over
the time period, such as unemployment and population size, may alter the
association between age composition and homicide rates. Several theoretical
perspectives have been used to explain the relationship between age and
crime, and I offer alternative interpretations of these approaches, which posit
the importance of particular moderating factors on the relationship between
age structure and homicide rates.
Phillips / U.S. Age Structure and Homicide Rates 233
Thus, the tack adopted here is distinct from that of previous research on
the relationship between age composition and crime. For example, Hirschi
and Gottfredson (1983) focus on one country, the United States, thereby controlling for all stable country characteristics over time, to posit that the basic
shape of age-specific crime rates does not vary across social and cultural conditions.1 In contrast, O’Brien, Stockard, and Isaacson (1999) and O’Brien
and Stockard (2002), noting the increasing concentration of criminal
involvement among the young during the late 1980s and early 1990s, estimate a modified age-period-cohort model, controlling for period characteristics that are stable across age groups, to investigate several cohort characteristics that may explain the shifts in the age-crime curves. The present study
controls for stable unmeasured county and period characteristics, but specifically examines the ways in which the association between age composition
and homicide rates within counties may be affected by differing socioeconomic conditions across counties over the time period.
Theoretical Explanations for a Relationship
between Age Structure and Homicide
The crude homicide rate (CHR) is determined by two factors: the schedule of age-specific homicide rates and the proportion of the population in a
particular age group. Because age-specific homicide offending and victimization rates are typically highest for young age groups (between the ages of
15 and 34), shifts in the relative size of the young population over time and
place necessarily produce changes in the crude homicide rate. However, to
the extent that the schedule of age-specific rates is affected by varying social
and economic conditions across time and place, the relative effect of the size
of the young population on homicide rates will differ across time and place.
A number of criminological theories purport to explain the familiar
inverted-J shaped pattern of age-specific homicide rates. Indeed, the association between an individual’s age and the propensity to commit crime is so
strong and well-established that one standard by which to assess the validity
of sociological theories of crime has been their ability to explain youth
involvement in crime and the subsequent drop-off with age (Greenberg
1977; Matza 1964; but see Hirschi and Gottfredson 1983). In particular,
three criminological schools of thought are commonly used to explain the
age-crime connection, namely elements of strain theory, social control theory, and cohort size theory (e.g., Greenberg 1977; O’Brien et al. 1999; Tittle
1988). These explanations for criminal behavior suggest that there are certain opportunities and motivations for crime commission that pertain more to
234 Journal of Research in Crime and Delinquency
the young population and thus lead to elevated criminal offending and victimization rates for these young age groups. To the extent that these opportunities and motivations for crime differ by time period and place, the pattern of
age-specific homicide rates may be affected and the effect of age structure on
crime rates should fluctuate accordingly.
I review below each of these criminological perspectives, with particular
attention to how they may explain youth involvement in crime.
Strain theory. Merton’s (1938) strain perspective emphasizes the process
whereby a disjunction between socially dictated goals and legitimate means
available to achieve those goals produces strain leading to deviance. Scholars
have offered several explanations for why strain may produce a pronounced
age-crime association at the individual level. Some argue that the more tenuous position of youth within the labor market relative to older people, coupled with often intense peer pressure to meet and achieve certain expectations and goals, may lure young people disproportionately into lucrative but
illegal activities (Greenberg 1977, 1985). The drop off in crime with age
occurs because youth eventually obtain legitimate employment, the returns
from employment increase as people age, and youth are removed from environments or circumstances that breed social pressures conducive to crime.
The strain or deprivation that youth may feel diminishes, leading them to
desist. Although more commonly applied to property crimes, strain theory
offers an explanation for violent crimes such as homicide, to the extent that
high levels of absolute and relative deprivation engender feelings of frustration and aggression that are ultimately manifested in violent behavior
(Dollard et al. 1939; Felson 1992).
Others note that among young men, those with poor economic prospects,
or increased strain, are more likely to engage in physical competition, violence, and alcohol abuse. Unlike economically advantaged young men who
can express their masculinity through economic achievement and other nonphysical behavior, economically disadvantaged men resort to violent behavior as a way to demonstrate their masculinity and to obtain respect (Gibbs
and Merighi 1994; Messerschmidt 1993). As a result, young males subject to
economic strain are more likely to respond with violence to verbal attacks
and honor contests.
Empirical evidence appears to support these suppositions. For example,
Anderson (1990) suggests that a scarcity of resources, a desire for the status
represented by some types of property in the youth population and a lack of
access to legitimate means of acquiring that status often translate into violence at an early age. Other research by Anderson (1999) notes that in poor
inner-city Black neighborhoods, young men feel the only way to maintain
Phillips / U.S. Age Structure and Homicide Rates 235
one’s respect and honor in the face of an attack or insult is to respond with
violence. Grogger (1998) contends that almost all of the age effect is a labor
market phenomenon by demonstrating that growth in wages with age is
largely responsible for the concurrent decline in crime. Others (Easterlin
1987; Friday and Hage 1976; Greenberg 1977; O’Brien et al. 1999; Steffensmeier et al. 1989) argue that changes in the socioeconomic status of adolescents and young adults during the past 50 years have promoted a strong agecrime relationship in recent decades.
Social control theory. Social control theory posits that strong social
bonds, as measured by feelings of attachment, involvement, commitment,
and belief, promote conformity (Hirschi 1969). With regard to the disproportionate involvement of youth in crime, some note that during the formative
years of adolescence and young adulthood, familial attachments and social
connections are loosened, social control is weakened, and the young are free
to violate group norms (O’Brien and Stockard 2002; Tittle 1988). Adolescents and young adults often break away and rebel against the authority of
their parents and school officials in an attempt to assert their own independence and identity. As young people eventually mature, obtain jobs, and form
their own families, strong social connections are resumed, leading in turn to
conformity.
Several scholars have applied tenets of social control theory to assert that
youth from single-parent households may be particularly vulnerable to criminal involvement. Children born to single mothers or those with divorced parents receive less direct monitoring and supervision of their behavior, simply
because of the absence of an additional adult in the household. A number of
individual-level studies support this notion. Children from single-parent
homes tend to receive less attention, which in turn is associated with higher
levels of delinquency among such children (e.g., Farrington 1989; Furstenberg and Hughes 1995; Hetherington, Cox, and Cox 1978; McLanahan and
Sandefur 1994; O’Brien et al. 1999). Furthermore, children from singleparent households are more likely to be economically disadvantaged, itself
an important predictor of delinquency (O’Brien et al. 1999; O’Hare 1996;
Savolainen 2000).
Relative cohort size. Whereas strain and social control theory are more
commonly applied to explain the age-crime association at the individual
level, Easterlin’s (1978, 1987) theory of relative cohort size more directly
addresses the aggregate relationship between age structure and crime. Rather
than assessing how changes in age composition affect crude rates of social
and economic behavior, Easterlin focuses instead on how cohort size may
236 Journal of Research in Crime and Delinquency
influence the schedule of age-specific rates of particular behaviors (Pampel
and Peters 1995). Some behaviors may become more common among certain age groups as a result of their relative cohort size.
In particular, Easterlin (1978) posits that relatively large cohorts face certain disadvantages, such as greater competition in the labor force, throughout
their life course. Members of large cohorts are thus more likely to encounter
unemployment, fewer opportunities for promotion, and lower wages in
adulthood due to this increased competition. Easterlin conjectures that this
economic deprivation may produce greater levels of criminal behavior
among such cohorts.
Easterlin (1978) focused primarily on the economic disadvantages faced
by large cohorts, but others note that relatively large cohorts also face socialpsychological disadvantages—they tend to be less socially integrated and
regulated within society (O’Brien 1989; O’Brien et al. 1999; Steffensmeier,
Streifel, and Shihadeh 1992). Reduced regulation of behavior occurs
through several different mechanisms: less attention and supervision from
parents, teachers, and other adults due to a higher child to adult ratio among
large cohorts during childhood and diminished access to resources, including forms of social capital. O’Brien et al. (1999) argue that the effects of
reduced social control are experienced by all members of the cohort, regardless of their own family status (see also Sampson 1987; Sampson and Wilson
1995). Communities with fewer intact families are less well integrated (due
to less time and available adults) and their institutions, such as churches and
schools, are overburdened. As a result, all members of larger cohorts are
more likely to experience feelings of pessimism and alienation, as well as
greater mental stress, feelings that in turn increase the propensity toward
crime.
Although Easterlin (1978) argued that the detrimental effects of large
cohort size persist throughout the life span, others assert that its effects may
be most pronounced at the younger ages (Kahn and Mason 1987; O’Brien
et al. 1999; Pampel and Gartner 1995). Kahn and Mason (1987), for example, argue that the effects of large cohort size on political alienation are especially strong for young adults. Young members of large cohorts eventually
alter their expectations and feelings of alienation subside once they have
encountered and then adjusted to the overcrowded labor market they face. In
fact, several studies demonstrate that although members of large cohorts initially face lower wages, they also experience faster wage growth. Such individuals may be more likely to invest in education to delay entry into a competitive labor force, and the labor force eventually absorbs the larger cohort
(Murphy et al. 1988; Smith and Welch 1981). These patterns enable the
wages of bigger cohorts to largely “catch up” to those of smaller cohorts.
Phillips / U.S. Age Structure and Homicide Rates 237
These arguments suggest that the effects of large cohort size may be particularly detrimental for adolescents and young adults. Thus, when the proportion of the population that is young is relatively large, we may find an
enhanced effect of age structure on crude homicide rates. Indeed, several
recent studies provide some indirect support for this notion. O’Brien and colleagues (1999, 2002) show that the increased concentration in recent years of
homicide offending and victimization among the young can be explained by
the relative size of cohorts and the degree of regulation these cohorts experience (measured by the percentage of cohort members born to unwed mothers). In their comparative study of 18 nations, Pampel and Gartner (1995)
demonstrate that greater levels of collectivism, defined as the relative development of national institutions for collective social protection, mitigates the
otherwise positive impact on homicide levels expected when youth comprise
a significant proportion of the population. The authors conclude that collectivist societies ease the transition of youth cohorts into adulthood and thus
are better able to buffer the possible harmful effect of membership in large
cohorts.
Hypotheses
I offer alternative ways to use these theories for identifying conditions that
may moderate the relationship between age composition and homicide rates.
As stated above, researchers have used strain and social control theory to
suggest that youth are particularly susceptible to criminal behavior when
confronted with high economic deprivation and low social control. These
theoretical applications are most commonly used to explain the individuallevel association between age and crime, but they also translate to the group
level—the aggregation of these individual effects often leads to group-level
differences (Firebaugh 1978; O’Brien et al. 1999). Hence, under conditions
of high economic deprivation and low social control, the relative concentration of criminal activity among the young may be more pronounced, leading
to a stronger effect of age composition on crude homicide rates. Alternatively, with less economic strain and greater social control, the association
between age and crime may be attenuated. Moreover, Easterlin’s (1978) theory of relative cohort size implies that to the extent that disadvantages disproportionately borne by members of larger cohorts, such as high levels of
unemployment or less social control, are reduced, the effect of age structure
on levels of violence may be weaker. In other words, in places where large
cohorts of young people face better opportunities and less stress, we may not
238 Journal of Research in Crime and Delinquency
see the same effect of age composition on crime rates (Pampel and Gartner
1995).
On the other hand, the above supposition that the young population is
most vulnerable to poor economic conditions and/or weak social control
may be incorrect. It could be the case that youth, the segment of the population already most exposed to relative economic deprivation and low social
control by the very nature of their position in the life course, are close to a
“saturation point” with regard to these factors. As a result, additional economic strain and/or less social control may have a relatively small effect on
youth propensity to commit crime compared to other age groups within the
population. In essence, under poor economic and social conditions, the older
segments of the population become subjected to more of the criminogenic
conditions that youth as a group routinely face. If so, the schedule of agespecific homicide rates would shift so that criminal activity is less heavily
concentrated in the young age ranges. Under this scenario, the positive association between age composition and homicide rates may be weakened in
places in which overall economic conditions are poor and/or social control is
reduced. That is, poor economic conditions provide greater motivations to
commit crime whereas weak social control offers greater opportunities for
crime, both of which extend to the population at large.
Data
This study is conducted at the county level using annual data for the
period 1970 to 1999. Counties provide a useful unit of analysis for the purposes of this research because they represent fairly small geographic areas
(compared to states), annual data for a number of indicators are available,
and the boundaries of large counties have not changed over time, unlike those
of Metropolitan Statistical Areas (MSAs) or central cities. However, note
that some argue that findings surrounding various theories of homicide
should not be affected by the unit of analysis selected (Parker, McCall, and
Land 1999). Violent crime, the outcome of interest, is measured with the
homicide rate. The analysis is restricted to homicide rates because homicide
data are the most accurate and complete of available crime data, unlike information on property crimes, which is plagued by problems of quality and
measurement (Cohen and Land 1987). Also, homicide is the crime least subject to changes in reporting over time, an important consideration given the
time-series nature of this analysis.
Data on homicide victims (excluding homicides due to legal intervention)
for the period 1970 to 1999 are obtained from the National Center for Health
Phillips / U.S. Age Structure and Homicide Rates 239
Statistics (NCHS); (U.S. Department of Health and Human Services 1999).
Because the NCHS does not provide geographical information for deaths
occurring in counties with populations of less than 100,000, the sample of
counties is restricted to those with a population of at least 100,000 throughout the entire period. The majority (80 percent to 85 percent) of annual
deaths from homicide in the United States occurred in these largest counties.
Although information on homicide perpetrators by county of occurrence
for the period 1976 to 1999 is available from the FBI’s Supplementary Homicide Reports (SHR), I chose to focus on homicide victims in this study for
several reasons. First, the quality of SHR data is questionable because not all
jurisdictions provide reports for each month, and for some incidents, the perpetrator is unknown. In addition, the efficacy of police departments to identify a perpetrator and make an arrest is likely to vary across counties and time,
and thus the use of information on perpetrators could introduce a potential
source of bias into the analysis. Second, a longer time series (1970 to 1999)
can be examined with victimization rates compared to offending rates (1976
to 1999). However, preliminary analyses using offending rates as the
dependent variable yielded results that are similar to those using victimization rates, which is not surprising given that the number of homicide victims
is measured by county of occurrence and the vast majority of homicide
incidents involve one victim and one perpetrator.
The denominator for the homicide victimization rate is the total mid–year
population of each county in each year. Data on population size are obtained
from the Census Bureau (U.S. Department of Commerce 1999). The Bureau
provides population counts by age (five–year intervals), sex, and race for
each census year (1970, 1980, 1990, and 2000) and inter-censal estimates of
population size for these demographic groups. The crude homicide rates are
logged to remove skewed data patterns.2
The independent variable of interest is the age composition of each
county’s population for each year. Both homicide victims and offenders are
heavily concentrated in the 15- to 34-year age group (note that the age distribution of victims peaks later than that for homicide offenders), and therefore,
age composition affects homicide rates through the production of both victims and offenders (Cohen and Land 1987). Age structure in the statistical
analysis is measured with two variables indicating the relative size of the
population that is young: The percentage aged 15 to 24 years and the percentage aged 25 to 34 years. Because the average age of homicide offenders and
victims is higher than for those of other crimes, the crime-prone age range is
extended to age 34. Information used to construct these measures of age
composition comes from the Census Bureau.
240 Journal of Research in Crime and Delinquency
Economic deprivation is strongly associated with levels of violent crime
(e.g., Blau and Blau 1982; Land, McCall, and Cohen 1990) and so, two variables that measure economic conditions across counties and time are
included: per capita income and the unemployment rate for each county in
each year. These particular measures are selected because information on
them is available for virtually all years under study. Data on per capita
income for each county from 1970 to 1999 are obtained from the Regional
Economic Information System (REIS); (U.S. Department of Commerce
2000). The per capita income figures are converted to 1982 to 1984 constant
dollars, using the regional Consumer Price Indices (CPI) available from the
Bureau of Labor Statistics (BLS) Website (U.S. Department of Commerce
1999). Data on unemployment levels, measured as the percentage of the
civilian labor force that is unemployed, at the county level are provided by
the BLS and are available for the year 1970 and annually from 1976 to 1999.
I use linear interpolation techniques assuming constant growth to estimate
unemployment rates for missing years (1971 to 1975).
Family structure has been identified as an important correlate of homicide
rates (e.g., Land et al. 1990; Sampson 1987). A measure of the percentage of
the population that is divorced is therefore included for each county and year
because other time-series analyses indicate that this particular measure is
associated with crime rates over time (Greenberg 2001). I gather this information from the Census Bureau for each census year (1970, 1980, 1990, and
2000) and apply linear interpolation techniques, assuming constant growth
over the period, to interpolate the missing values for the inter-censal years.
Finally, several standard control variables, obtained from the Census
Bureau, are incorporated into the analyses. A measure of the population size
of each county in each year is included. Not only do larger populations present a greater number of potential targets for criminals but also sociologists
have long recognized the positive relationship between a place’s size and
some forms of social disorganization, such as criminal activity (Wirth 1969).
In addition, a measure of the relative size of the male population (percentage
male) across time and place is included because violence is much more common among men. The race composition of each county is controlled, with a
variable measuring the percentage of the population that is Black, as we
know the incidence of homicide victimization and offending is greater
among this demographic group. In all analyses, the measure of county population size is logged to remove a nonlinear association with homicide rates.
Table 1 displays descriptive statistics for these variables, showing the
mean values as well as overall, temporal, and spatial variation in these characteristics. Note that there is ample variation in these characteristics within
Phillips / U.S. Age Structure and Homicide Rates 241
Table 1
Descriptive Statistics for Dependent and Independent Variables
Variable
Crude homicide rate
per 100,000
Percent divorced
Percent unemployed
Per capita income
(000s) (82-84 $)
Percent aged 15-24
Percent aged 25-34
Percent male
Percent Black
Population size (0000)
Year
Number of
Observations
Mean
Overall
Standard Deviations
Temporal
Spatial
12,120
7.729
7.996
3.259
7.302
12,120
12,076
12,120
6.924
6.193
13.643
2.616
2.639
3.234
2.091
1.937
2.026
1.572
1.793
2.521
12,120
12,120
12,120
12,120
12,120
12,120
17.009
15.982
48.739
10.647
41.333
84.500
3.737
2.451
1.269
11.704
60.700
8.656
2.306
1.736
0.331
1.815
10.127
8.656
2.940
1.730
1.225
11.563
59.849
0.000
Note: Based on 404 U.S. counties for the 1970-1999 period. Temporal variation measures
within-county variation in these characteristics while spatial variation measures between-county
variation.
counties over time. In particular, the proportion young changes quite substantially over time—a standard deviation of 2.3 and 1.7 percentage points
for the percentage aged 15 to 24 and 25 to 34, respectively.
Method
To determine the association between age structure and homicide levels
within counties over time, I construct a cross-sectional time-series data set,
containing repeated measurements on counties over time, and estimate a
model of the following general form (Johnston and DiNardo 1997;
Wooldridge 2002).
Yjt = α + Xjt β + νj + τt + εjt
The dependent variable Yjt represents the logged Crude Homicide Rate
(CHR) in time t for county j. α denotes the model intercept and β represents
the estimated set of parameters for Xjt, the matrix of independent variables for
each county j and year t. The model includes a county-specific residual, νj,
which varies across counties but not across time and allows for correlation
242 Journal of Research in Crime and Delinquency
among observations from the same county. Period effects in homicide levels
are controlled by including a dummy variable for year, τt. εjt is the model
residual and captures random variation within counties over time.
A fixed-effects approach is adopted to estimate equation (1). Dummy
variables for all counties (less one) are included in all models, which is equivalent to expressing all variables as deviations from their county-specific
means (Johnston and DiNardo 1997). Essentially, the fixed-effects model
treats νj, the between-county residuals, as fixed and estimable and provides
estimates only for the within-county estimators (variables for which values
differ from year to year within a county). This model is advantageous for several reasons. Most notably, estimation bias is reduced because the fixedeffects model controls for all stable unmeasured county characteristics and
omitted aspects of time periods common to all counties, thus providing a
more rigorous test of the factors associated with homicide rates (Hsiao 2003;
Johnston and DiNardo 1997; see study limitations of article for further
discussion).
Because nonstationary time series can lead to spurious regression results
in panel studies, tests for the stationarity of the various time-series included
in this analysis were conducted, using the Levin-Lin-Chu test and alternate
lag-lengths ranging from one to eight for all series (Levin, Lin, and Chu
2002; Liedka et al., 2001). The null hypothesis of nonstationarity for all
series was virtually always rejected, with the exception of three cases (the
percentage divorced, the percentage aged 25 to 34, and per capita income). A
graphical inspection of these three variables indicated that these series are
trend-stationary. Because the models include a dummy variable for year, thus
controlling for time trends, the nonstationarity of these series is partialed out.
Note that these tests should be treated with caution because the properties of
variables are being tested on a very short time-series, thus reducing the
effectiveness of the test.
Exploratory analyses revealed that an autoregressive covariance structure
fit better than one constraining all residuals within counties to be equal (chisquare = 278.6, df = 1). In addition, tests indicated the presence of
heteroskedasticity across counties (chi-square = 3,593.67, df = 403). Thus,
the xtgls command in Stata, which allows estimation in the presence of
AR(1) autocorrelation within counties and heteroskedasticity across counties, is applied to estimate all models, using an iterated generalized least
squares estimator.3
Phillips / U.S. Age Structure and Homicide Rates 243
Analysis
I begin by estimating a general model of U.S. county homicide victimization rates to determine whether a strong relationship between the relative size
of the young population and homicide rates persists at a more disaggregated
level of analysis. The hypotheses that the effect of age composition on homicide rates across county and year may be affected by social and economic
conditions are then tested. The average levels of economic deprivation (captured by unemployment rates and per capita income) and social control
(proxied by the percentage divorced and population size) for each county
over the entire period are calculated and interacted with the variable measuring age composition. Note that a couple of these variables, in particular,
unemployment rates and the percentage divorced, can be viewed as measures
of both economic strain and social control. For example, high unemployment may contribute both to economic deprivation and to weak social
connections.
A model that includes an interaction between age composition and time
period is also estimated to determine whether the effect of age structure on
homicide levels varies by period. This model is of particular interest given
the sharp rise in violent youth offending during the late 1980s and early
1990s. Scholars attribute this rise to increased handgun availability during
this period and to the emergence of crack cocaine in large cities (Blumstein
and Wallman 2000; Cook and Laub 1998). Grogger (2000), for example,
notes that the crack trade offered an economic opportunity for young disadvantaged men in the face of declining legitimate jobs during the 1980s and
early 1990s. In contrast, the U.S. economy was thriving by the mid-to-late
1990s. Therefore, interactions with time period offer an alternative way to
determine whether differing economic and social conditions affect the relationship between age composition and homicide rates.
Results
Results from the estimation of the fixed-effects models are displayed in
Table 2.4 Model 1 displays estimates of only the main effects of the variables
included in the analysis. Consistent with national-level studies of the temporal association between age structure and homicide rates in the United States
(e.g., Cohen and Land 1987; Gartner and Parker 1990), I find a positive association between the proportion young and homicide rates within U.S.
counties over time. On average, a one-percentage point increase in the size
of the populations aged 15 to 24 and 25 to 34 is associated with a 1.1 percent
244
(0.005)
(0.005)
(0.005)
(0.002)
(0.003)
(0.011)
(0.002)
(0.026)
0.011**
0.013**
0.016**
–0.017**
–0.012**
0.036**
0.018**
–0.294**
4,406.10
0.557
SE
1.999
Coefficient
(0.001)
(0.001)
–0.004**
0.001
4,386.328
(0.011)
(0.002)
(0.026)
(0.006)
(0.002)
(0.003)
(0.008)
(0.009)
0.587
SE
0.022*
0.017**
–0.311**
0.003
–0.016**
–0.010**
0.042**
0.009
2.853
Coefficient
Model 2
(0.002)
(0.002)
(0.011)
(0.002)
(0.046)
(0.005)
(0.002)
(0.003)
(0.021)
(0.023)
0.739
SE
4,341.18
–0.007**
0.015**
0.029
0.014**
–0.413**
0.024**
–0.016**
–0.013**
0.087**
–0.190**
4.055
Coefficient
Model 3
(0.001)
(0.001)
(0.011)
(0.002)
(0.026)
(0.005)
(0.002)
(0.004)
(0.011)
(0.011)
0.573
SE
4,399.24
0.002**
0.001**
0.042**
0.018**
–0.298**
0.013**
–0.016**
–0.008**
–0.013
–0.008
1.818
Coefficient
Model 4
(0.005)
(0.002)
(0.003)
(0.007)
(0.008)
0.739
SE
0.000
(0.001)
0.007** (0.001)
4,372.2
0.037** (0.011)
0.017** (0.002)
–0.279** –(0.026)
0.018**
–0.019**
–0.010**
0.011
–0.025**
4.055
Coefficient
Model 5
Note: County and year dummies are included in all models but their parameter estimates are not displayed. Number of observations = 12,076.
*p < .10. **p < .05.
Intercept
Main effects
Percentage aged 15-24 years
Percentage aged 25-34 years
Socioeconomic characteristics
Percent divorced
Unemployment rate
Per capita income (000) (82-84$)
Demographic controls
Percentage male
Percentage Black
Logged population size
Interactions With Age Measures
Average percentage divorced*
Percentage aged 15-24 years
Percentage aged 25- 34 years
Average logged population size*
Percentage aged 15-24 years
Percentage aged 25-34 years
Average per capita income (000)*
Percentage aged 15-24 years
Percentage aged 25-34 years
Average unemployment rate*
Percentage Aged 15-24 years
Percentage Aged 25-34 years
–2 log likelihood
Variable
Model 1
Table 2
Fixed County and Year Effects Models of Logged Homicide Rate on Selected Covariates, 1970-1999
Phillips / U.S. Age Structure and Homicide Rates 245
(= e0.011 – 1) and a 1.3 percent (= e0.013 – 1) rise, respectively, in the homicide
rate.5 Put another way, an increase of one standard deviation in the relative
size of the populations aged 15 to 24 and 25 to 34 within counties over time is
associated with a 2.6 percent (= e0.026 – 1) and a 2.3 percent (e0.023 – 1) rise,
respectively in the homicide rate.
Shifts in socioeconomic conditions within counties are also associated
with homicide rates. On average, higher levels of the percentage of the population divorced are associated with larger homicide rate within counties over
time. The unemployment rate is negatively associated with homicide victimization rates—a one-percentage point increase in the unemployment rate is
associated with a 1.7 percent decline in the homicide rate. This result is consistent with findings showing that the contemporaneous effect of unemployment on homicide rates can be negative because opportunities for crime may
be diminished (e.g., Cantor and Land 1985). As predicted by strain theory,
increases in per capita income are associated with declines in the homicide
rate within counties over time.
Several of the demographic controls are important predictors of variation
in county homicide rates. Increases in both the percentage of the population
that is Black and male are positively related to homicide rates within counties
over time. Although numerous studies demonstrate a positive cross-sectional
association between population size and levels of violence (see Land et al.
1990), variation in population size is inversely associated with variation in
homicide rates over time. In other words, population growth is associated
with drops in homicide rates.6
Models 2 to 5 of Table 2 address the second objective of this study, namely
to determine whether the positive association between age composition and
homicide victimization rates documented in Model 1 is affected by varying
socioeconomic conditions. Again, socioeconomic conditions are measured
by calculating the average levels of the percentage divorced, population size,
per capita income, and unemployment over the study period for each county.7
Note that the average levels of population size and unemployment rates are
positively associated with homicide rates across counties, similar to findings
of cross-sectional studies of homicide and unlike the temporal relationship
shown above (see Phillips, forthcoming, for more detail). Therefore, larger
average population size and higher average unemployment and divorce over
the period indicate lower levels of social control and higher levels of economic deprivation; higher average per capita income suggests lower levels of
economic deprivation.
Model 2, which uses the average percentage divorced within each county
over the study period as a proxy both for levels of social control and strain,
shows a statistically significant negative interaction between the percentage
246 Journal of Research in Crime and Delinquency
Figure 1
Effect of Temporal Variation in the Percentage Aged 15 to 24 on
Crude Homicide Rates (CHR), by Percentage Divorced in County
8%
Net Percentage Change in CHR
6%
4%
2%
0%
-1
0
1
-2%
-4%
-6%
-8%
One Standard Deviation Change in Percentage Aged 15-24
Low Percent Divorced
Average Percent Divorced
High Percent Divorced
aged 15 to 24 and the average percentage divorced. The positive association
between variation in the percentage young and crude homicide rates is
greater in counties with lower levels of divorce. Figure 1 displays this interaction, showing the estimated net effect on the crude homicide rate of temporal variation in the percentage young in the counties with the lowest, average,
and highest levels of divorce over the period, and suggests that these interaction effects are substantively important. A one-standard deviation increase in
the percentage aged 15 to 24 has a negative association with the crude homicide rate in the county with the highest level of divorce over the period; the
homicide rate is predicted to decline by about 2 percent with such a change in
the percentage aged 15 to 24. The corresponding effect on the homicide rate
in the county with the lowest average level of divorce is estimated to be a rise
of about 7 percent (see Figure 1).
A significant negative interaction is also found between average population size of counties over the period (primarily a measure of social control)
and variation in the percentage aged 15 to 24. That is, a greater positive effect
of increases in the percentage aged 15 to 24 on homicide rates is found in
smaller counties. Figure 2 indicates that in counties with the largest populations, variation in the percentage aged 15 to 24 has a strong negative association with the crude homicide rate. However, in the smallest counties, a posi-
Phillips / U.S. Age Structure and Homicide Rates 247
Figure 2
Effect of Temporal Variation in the Percentage Aged 15 to 24 on
Crude Homicide Rates (CHR), by Population Size of County
5%
Net Percentage Change in CHR
4%
3%
2%
1%
0%
-1
0
1
-1%
-2%
-3%
-4%
-5%
One Standard Deviation Change in Percentage Aged 15-24
Low Pop Size
Average Pop Size
High Pop Size
tive association between the percentage aged 15 to 24 and the homicide rate
exists—a one-standard deviation increase in the percentage aged 15 to 24 is
associated with about a 3 percent rise in the crude homicide rate. Interestingly, the opposite is true for the effect of the percentage aged 25 to 34. The
percentage aged 25 to 34 has a stronger positive association with homicide
rates in the largest counties (see Figure 3). A one-standard deviation increase
in the percentage aged 25 to 34 is associated with about a 10 percent rise in
the crude homicide rate in large counties, but with about a 2 percent decline
in small counties.
Model 4 examines whether the association between age structure and
homicide victimization rates varies by economic conditions. I find evidence
that the relationship between age structure and homicide rates is affected by
differing economic conditions, as measured by average per capita income of
counties over the period. Whereas a one-standard deviation change in the
percentage aged 15 to 24 results in virtually no change in the crude homicide
rate in the county with the lowest levels of per capita income over the period,
the association is positive and considerably stronger in counties with higher
per capita income. In counties with average levels of per capita income over
the period, a one-standard deviation increase in the percentage young is associated with about a 2 percent increase in the crude homicide rate, but in the
wealthiest counties, such a change in the proportion young is associated with
248 Journal of Research in Crime and Delinquency
Figure 3
Effect of Temporal Variation in the Percentage Aged 25 to 34 on
Crude Homicide Rates (CHR), by Population Size of County
Net Percentage Change in CHR
15%
10%
5%
0%
-1
0
1
-5%
-10%
One Standard Deviation Change in Percentage Aged 25-34
Low Pop Size
Average Pop Size
High Pop Size
an 8 percent increase in homicide rates (see Figure 4). Patterns of variation in
the association between the percentage aged 25 to 34, the older portion of the
crime-prone age range, and homicide rates by level of per capita income are
similar.
Model 5 explores whether the association between age structure and
homicide rates varies according to another indicator of economic conditions
and social control, namely unemployment rates. Although the association
between the percentage aged 15 to 24 and homicide rates does not vary by
average unemployment level, there is evidence that increases over time in the
percentage aged 25 to 34 have a stronger association with homicide rates in
counties with higher average unemployment rates. Figure 5 indicates that a
one-standard deviation increase in the percentage aged 25 to 34 over time is
associated with almost a 15 percent rise in the crude homicide rate in the U.S.
counties with the highest unemployment levels.8
Finally, I examine whether the effect of the relative size of the young population on homicide rates varies by time period. For parsimony, six time periods (1970 to 1974, 1975 to 1979, 1980 to 1984, 1985 to 1989, 1990 to 1994,
and 1995 to 1999) are identified instead of including 30 year-dummies and
the corresponding interactions with the age-structure measures. As shown in
Table 3, there are some statistically significant differences in the effect of
changes in the relative size of the population aged 15 to 24 and 25 to 34 by
Phillips / U.S. Age Structure and Homicide Rates 249
Figure 4
Effect of Temporal Variation in the Percentage Aged 15 to 24 on
Crude Homicide Rates (CHR), by Per Capita Income of County
10%
Net Percentage Change in CHR
8%
6%
4%
2%
0%
-1
0
1
-2%
-4%
-6%
-8%
-10%
One Standard Deviation Change in Percentage Aged 15-24
Low Per Capita Income
Average Per Capita Income
High Per Capita Income
Figure 5
Effect of Temporal Variation in the Percentage Aged 25 to 34 on
Crude Homicide Rates (CHR), by Unemployment Level of County
Net Percentage Change in CHR
20%
15%
10%
5%
0%
-1
0
1
-5%
-10%
-15%
One Standard Deviation Change in Percentage Aged 25-34
Low Unemployment
Average Unemployment
High Unemployment
250 Journal of Research in Crime and Delinquency
Table 3
Period Effects of Age Structure on
Logged Homicide Rates, 1970 to 1999
Variable
Intercept
Main effects
Percentage aged 15-24 years
Percentage aged 25-34 years
Socioeconomic characteristics
Percentage divorced
Unemployment rate
Per capita income (000) (82-84$)
Demographic controls
Percentage male
Logged percentage Black
Logged population size
Time period (Reference = 1995-1999)
1970-1974
1975-1979
1980-1984
1985-1989
1990-1994
Interactions with age measures
Percentage aged 15-24*
1970-1974
1975-1979
1980-1984
1985-1989
1990-1994
Percentage aged 25-34*
1970-1974
1975-1979
1980-1984
1985-1989
1990-1994
Coefficient
Standard Error
1.960**
0.586
0.033**
0.043**
0.005
0.005
0.015**
–0.014**
–0.022**
0.005
0.002
0.003
0.022**
0.015**
–0.276**
0.011
0.002
0.025
0.116
0.403**
0.533**
0.392**
0.338**
0.104
0.105
0.106
0.104
0.095
–0.003
–0.007*
–0.008*
–0.016**
–0.002
0.004
0.004
0.004
0.004
0.004
–0.005
–0.020**
–0.028**
–0.013**
–0.012**
0.006
0.006
0.006
0.006
0.005
Note: County dummies are included in the model but their parameter estimates are not displayed.
Number of observations = 12,076.
*p < .10. **p < .05.
time period. Goodness-of-fit criteria indicate that the model including interactions between age composition and time period fits significantly better
than one excluding them (chi-square = 33.9, df = 10).
In particular, after controlling for social, economic, and other demographic characteristics of the counties and time periods, the results reveal
Phillips / U.S. Age Structure and Homicide Rates 251
that the positive association between homicide rates and the percentage aged
15 to 24 years was reduced between the mid-1970s and late 1980s. A onepercentage point increase in the size of the population aged 15 to 24 years is
estimated to be associated with a 3.3 percent rise in the crude homicide rate
between 1995 and 1999, but with a 1.7 percent for the years 1985 to 1989,
respectively. This difference is statistically significant, although not substantively large. The results also indicate that the effect on homicide rates of
increases in the percentage aged 25 to 34 is less during the late 1970s through
the early 1990s relative to the most recent period, 1995 to 1999. For example,
an increase of one percentage point in those aged 25 to 34 is associated with
an increase of 4.3 percent in the homicide rate during the most recent period,
but such a rise leads to only a 1.5 percent in homicide rates during the 1980 to
1984 period.9
Discussion
This study examines the nature of the association between age composition and homicide victimization rates in the United States during the last
three decades of the twentieth century. The results indicate that a positive
temporal association between the proportion young and homicide rates
exists within U.S. counties, consistent with findings based on the country as a
whole. However, the results indicate that the direction and strength of this
average association between age composition and homicide within counties
is altered by several social and economic conditions. In particular, the
strength of the association between the percentage aged 15 to 24 years and
homicide rates within counties is reduced in counties with low social control,
approximated using percentage divorced and population size. There is also
evidence that the association between the percentage young and homicide
rates is attenuated within counties with high levels of economic deprivation,
as measured by per capita income. With regard to the association between the
percentage aged 25 to 34 and homicide rates, however, the findings indicate
that sometimes, the opposite pattern exists. The positive association may be
stronger within counties that are larger and have higher average unemployment levels, that is, in counties with less social control and greater economic
deprivation. Finally, period effects to the relationship between age composition and homicide rates are observed, with increases in the percentage young
generally having a larger positive association with homicide rates in the most
recent period, 1995 to 1999, relative to the 1970s and 1980s.
I began this study with two opposing hypotheses about the ways in which
such social and economic conditions may affect the association between age
252 Journal of Research in Crime and Delinquency
structure and homicide rates. Certainly, the results regarding the younger
range of the youth population, namely those aged 15 to 24 years, are consistent with the supposition that the association between the percentage young
and homicide rates is mitigated when other criminogenic forces are present.
In counties with relatively low social control and high economic deprivation,
all segments of the population, not just the young, are more likely to be
exposed to conditions conducive to crime. It follows that such counties may
exhibit age distributions of criminal activity that are less heavily concentrated in the young age ranges.10 As a result, the positive association between
changes in the percentage young and homicide rates is reduced under these
conditions.11
In other words, the analysis reveals that certain criminogenic forces, such
as poor social and economic conditions that operate to increase crime rates,
can attenuate the positive association between the percentage aged 15 to 24
and homicide rates. Indeed, some of the observed period effects to the relationship between the relative size of the young population and homicide rates
are consistent with this premise. For example, the mid-to-late 1990s were a
period with relatively few criminogenic forces at work—the economy was
booming and drug markets had waned. In contrast, the mid-to-late 1980s
were a period with socioeconomic conditions conducive to crime, and indeed
we find a reduced effect of the percentage aged 15 to 24 on homicide rates
during this time.
However, it is interesting to note that the attenuated effect of age composition on homicide rates mostly pertains to only the younger portion of the
crime-prone age range, those aged 15 to 24. Indeed, some of the analyses
suggest that the association between the percentage aged 25 to 34 and homicide rates is increased when criminogenic conditions prevail. For example,
the positive association between the percentage aged 25 to 34 and homicide
rates is greater in counties with weaker social control and higher economic
deprivation (as measured by population size and unemployment levels). Perhaps this pattern is due to the fact that strain and social control theories may
be more relevant as an explanation for the involvement of adolescents and
younger adults (less than 25 years of age) in criminal activity. The older portion of the young population (ages 25 to 34) as a group are less subjected to
economic and social strain because they are more likely to have established
job stability and to have married. Data from the mid-1990s indicate, for
example, that almost 80 percent of individuals aged 25 to 34 are employed
and 58 percent are married; the comparable figures for the younger age group
are about 58 percent (ages 16 to 24) and 18 percent (ages 18 to 24) (http://
ferret.bls.census.gov/macro/171996/empearn/3_000.htm). Thus, it may be
that a “saturation point” has not been reached for this segment of the popula-
Phillips / U.S. Age Structure and Homicide Rates 253
tion. Rather, a greater prevalence of criminogenic conditions within places
disproportionately affects the behavior of those in the older range of the
youth population, thus leading to a stronger association. Further investigation of these findings and the mechanisms underlying them is warranted in
future research.
Another intriguing result relates to the negative associations of unemployment and population size with homicide rates, effects that run contrary
to common theoretical expectations. Most previous studies examine the relationship between these factors and crime rates using a cross-sectional
approach and report positive effects of these factors on crime (e.g., Land
et al. 1990). However, Hsiao (2003) notes that cross-sectional studies tend to
measure long-run effects, but time-series analyses typically capture shortterm fluctuations. Thus, to the extent that short-term effects of these factors
are distinct from those in the long term, the negative associations found
within counties over time may be expected.
For example, with regard to unemployment, strain theory suggests that
unemployment may raise the motivation to commit crime, but routine activity theory suggests that unemployment reduces opportunities for crime due
to increased guardianship (Cantor and Land 1985; see also the symposium in
the Journal of Quantitative Criminology 2001). Although the opportunity
effects of unemployment rates on crime levels are likely to be relatively
immediate, the motivational aspects are typically delayed, leading to different effects of unemployment on crime in the short and long term (Cantor and
Land 1985; Land, Cantor, and Russell 1995). With regard to population size,
in the long term, larger places may promote social disorganization and anomie, factors that are associated with higher levels of violence. In the short
term, however, population growth (e.g., in-migration) may reflect the general desirability and economic well-being of a place, characteristics that we
expect would drive down crime rates (see Phillips, forthcoming, for further
discussion).
Study Limitations
Several limitations of this study should be noted. First, the analysis is
based only on large counties in the United States. The NCHS does not provide geographic information on deaths occurring in places with a population
size fewer than 100,000 after 1981. Although victimization data from the
SHR are available for these smaller counties after 1981, they were not used
because research suggests that victimization data from these two sources
may not be entirely compatible at the state or county level (Reidel 1999).
254 Journal of Research in Crime and Delinquency
Moreover, the boundaries of many small counties changed over the study
period and cannot be reconstructed. On average, these larger U.S. counties
have higher levels of homicide over the study period. Their populations are
typically wealthier and less likely to be unemployed but more likely to be
divorced; in terms of demographic structure, these counties are younger and
more heterogeneous (racial composition). Thus, the generalizability of the
study results may be limited in some respects.
Second, there is potential for omitted variable bias.12 Most notably, we
might expect that sanction variables, such as criminal justice laws, incarceration rates, or police per capita, may be associated with homicide rates within
counties over time. However, these variables are not included as they are
likely to be endogenous with homicide rates (e.g., Levitt 1996; Liedka et al.
2001; Marvell and Moody 1996), and such endogeneity leads to inconsistent
estimates (Wooldridge 2002). The most common method for dealing with
this issue is the instrumental variable approach, but finding an appropriate
instrument for these variables at the county level for the time period investigated is very difficult and the use of a poor instrument may only exacerbate
the problem of bias (see Liedka et al. 2001; Wooldridge 2002, for more
detail).
Finally, although typically ignored in time-series cross-sectional work,
future research should make attempts to consider the possible effect of spatial autocorrelation in the error term because changes within a county in the
homicide rate over time may produce changes in surrounding counties.
About 45 percent of the 404 counties in the present sample belong to one of
63 metropolitan areas (although the remaining 55 percent of counties are not
adjacent to any other counties in the sample). Controls for spatial
autocorrelation are not included in the present analysis for several reasons.
First, it is not possible to estimate spatial disturbance models with an
autoregressive structure in SAS or Stata (personal communication with the
SAS Institute and Stata Corporation; see also Worrall and Pratt, 2004).13 In
addition, any diffusion effects of violence are likely to be most relevant to the
areas immediately adjacent (i.e., within the first few miles) to a county’s border. Data limitations clearly preclude such an examination in this case.
It is important to note, however, that the fixed-effects estimation procedure used in this study mitigates the potential effect of these limitations. With
regard to possible omitted variable bias, Johnston and DiNardo (1997) make
the following point: “panel data estimation has grown in popularity because
it has held out the promise of reducing a grave problem faced by many
researchers: the lack of an adequate list of independent variables to explain
the dependent variable” (p. 395). Pertaining to this application, county dummies capture the effect of unmeasured county characteristics that are stable
Phillips / U.S. Age Structure and Homicide Rates 255
over time, and we might expect this to be largely true for certain sanction
variables such as gun control or capital punishment laws. The time period
dummies control for the effect of omitted variables that have a uniform effect
on all counties over time. Thus, to some extent, the time dummies may pick
up some of the national trend in incarceration rates over the period. With
regard to spatial autocorrelation, the fixed effects approach controls for (stable) omitted characteristics common to counties clustered in the same metropolitan area or state, thereby partially controlling for spatial autocorrelation.
Conclusion
Despite some limitations, this article improves our understanding of a key
relationship within criminology, namely that between age composition and
violent crime rates. Criminologists often rely on demographic forecasts,
such as expected changes in age composition, as a means to predict future
crime trends (e.g., Fox 1996). Given the study results suggesting that the age
structure-homicide association can be affected by varying socioeconomic
conditions, this approach may not always be appropriate. For example, in
areas with other criminogenic forces at play (e.g., high levels of economic
deprivation and/or low levels of social control), increases in the relative size
of the young (those aged 15 to 24) may not necessarily generate increased
crime levels. On the other hand, increases in the relative size of those aged 25
to 34 may indeed contribute to higher homicide levels under such conditions.
Notes
1. Note that Hirschi and Gottfredson (1983) acknowledge that the magnitude of rates across
such conditions may vary (see also Britt 1992). This thesis generated a large number of studies,
the majority of which conclude that the premise is overstated (e.g., Farrington 1986; Greenberg
1985; Steffensmeier et al. 1989).
2. About 2.7 percent of cases had a homicide rate of 0. A small value (1) was added to the
homicide rate so that the log transformation could be performed (see Hamilton 1992, p. 17).
3. In exploratory analyses, a negative binomial model was estimated for comparison purposes; the substantive conclusions drawn from that model are similar to those presented in this
article.
4. The data set includes information on 404 counties for a period of 30 years (12,120 observations). The final analysis contains data on 12,076 observations due to missing unemployment
data for 44 county-years.
5. The percentage changes reported using the formula 100(eb – 1) are approximate assuming an underlying unreported baseline homicide mortality rate of 1 per 100,000.
6. Tests for multicollinearity with models using panel data and an autoregressive error structure are not straightforward, but multicollinearity does not appear to pose a serious problem for
256 Journal of Research in Crime and Delinquency
several reasons. First, a benefit of panel data is to lessen the problem of multicollinearity (Hsiao
2003, pp. 311-12). Second, the main problem presented by multicollinearity is inflated standard
errors leading to statistically insignificant effects, but all the variables included in this analysis
are significant at the 5 percent level.
7. These particular measures are used instead of contemporaneous indicators to reduce
problems of multicollinearity and to facilitate interpretation of results. The main effects of these
variables do not appear in the models because they are subsumed by the county-fixed effects.
8. Analyses were also conducted employing five-year age groups (ages 15 to 19, 20 to 24, 25
to 29, and 30 to 34), but because a comparison of the Bayesian Information Criteria (BIC) statistics indicated that the model with two 10-year age groups is a better, more parsimonious fit, I
present those results in this article. Note however that the findings from the two different model
specifications are very similar. In some cases, I found that the interactions between the percentage aged 15 to 24 and social and/or economic conditions are largely driven by the 20- to 24-year
age bracket. I also examined whether there is an association between the percentages aged 35 to
44, 45 to 54, and 55 to 64 and homicide rates but found no significant relationship.
9. Additional tests indicate that there is no statistically significant difference (at p < .05) in
the relationship between the percentage aged 15 to 24 years and homicide rates between 1975
and 1989. The association between the percentage aged 25 to 34 and homicide rates during the
period 1975 to 1984 differs significantly from that during the period 1985 to 1994.
10. Counties with high economic deprivation and low social control are expected to have the
same basic inverted-J shaped age distribution of crime, but the proportionate share in the young
age ranges is somewhat less than in counties with low economic deprivation and high social
control.
11. Although Hirschi and Gottfredson (1983) do not directly address the relationship
between a population’s age composition and crime rates, their age-invariance thesis has implications for this relationship. If the shape of the age-crime curve does not differ, changes in a population’s age structure should have the same effect on crime rates over time and place. (Note, however, that the opposite relationship does not hold; consistent effects of a population’s age
structure on crime rates over time and place do not necessarily mean that the schedule of crime
rates is invariant.) Thus, the finding here, that there are differences across counties in the temporal association between the relative size of the young population and homicide rates, implies that
the age-specific schedule of homicide rates differs across counties. This result is at odds with the
Hirschi and Gottfredson thesis.
12. Despite the many advantages to panel research designs, a drawback is the difficulty in
obtaining detailed data on a number of different variables for cross-sections over a long period of
time. I imposed fairly strict standards on the quality of data examined; with the exception of
divorce levels, all variables are available annually for almost all the years under study.
13. Worrall and Pratt (2004) found in their analysis of crime across all counties in California
that results controlling for spatial clustering were virtually identical to those without controls for
spatial autocorrelation.
References
Anderson, Elijah. 1990. Streetwise: Race, Class and Change in an Urban Community. Chicago:
University of Chicago Press.
⎯⎯⎯. 1999. Code of the Street. New York: Norton.
Blau, Judith R. and Peter M. Blau. 1982. “The Cost of Inequality: Metropolitan Structure and
Violent Crime.” American Sociological Review 47:114–29.
Phillips / U.S. Age Structure and Homicide Rates 257
Blumstein, Alfred and Joel Wallman. 2000. The Crime Drop in America. Cambridge, UK: Cambridge University Press.
Britt, Chester L. 1992. “Constancy and Change in the U.S. Age Distribution of Crime: A Test of
the ‘Invariance Hypothesis’.” Journal of Quantitative Criminology 8 (2): 175-87.
Cantor, David and Kenneth C. Land. 1985. “Unemployment and Crime Rates in the Post-World
War II United States: A Theoretical and Empirical Analysis.” American Sociological Review
50:317-32.
Cohen, Lawrence E. and Kenneth C. Land. 1987. “Age Structure and Crime: Symmetry versus
Asymmetry and the Projection of Crime Rates through the 1990s.” American Sociological
Review 52:180-83.
Cook, Philip J. and John H. Laub. 1998. “The Unprecedented Epidemic in Youth Violence.” Pp.
27-64 in Crime and Justice: A Review of Research, Vol. 24, edited by Norval Morris and
Michael Tonry. Chicago: University of Chicago Press.
Dollard, John, Leonard W. Doob, Neal E. Miller, O. H. Mowrer, and Robert R. Sears. 1939. Frustration and Aggression. New Haven, CT: Yale University Press.
Easterlin, Richard. 1978. “What Will 1984 Be Like? Socioeconomic Implications of Recent
Twists in Age Structure.” Demography 15:397-421.
⎯⎯⎯. 1987. Birth and Fortune: The Impact of Numbers on Personal Welfare. Chicago: University of Chicago Press.
Farrington, David. 1989. “Early Predictors of Adolescent Aggression and Adult Violence.” Violence and Victims 4 (2): 79-100.
Felson, Richard B. 1992. “Kick ’em When They’re Down.” The Sociological Quarterly 33:1-16.
Ferdinand, Theodore N. 1970. “Demographic Shifts and Criminality: An Inquiry.” British Journal of Criminology 10:169-75.
Firebaugh, Glenn. 1978. “A Rule for Inferring Individual-Level Relationships from Aggregate
Data.” American Sociological Review, 43 (4): 557-72.
Fox, James A. 1996. Trends in Juvenile Violence: A Report to the U.S. Attorney General on Current and Future Rates of Juvenile Offending. Washington, DC: Bureau of Justice Statistics.
Friday, Paul and Jerald Hage. 1976. “Youth Crime in Postindustrial Societies: An Integrated Perspective.” Criminology 14:347-68.
Furstenberg, Frank F. Jr. and Mary Elizabeth Hughes. 1995. “Social Capital and Successful
Development among At-Risk Youth.” Journal of Marriage and the Family 57:580-92.
Gartner, Rosemary. 1990. “The Victims of Homicide: A Temporal and Cross-National Comparison.” American Sociological Review 53:92-106.
Gartner, Rosemary and Robert Nash Parker. 1990. “Cross-National Evidence on Homicide and
the Age Structure of the Population.” Social Forces 69 (2): 351-71.
Gibbs, Jewelle Taylor and Joseph R. Merighi. 1994. “Young Black Males: Marginality, Masculinity, and Criminality.” In Just Boys Doing Business? Men, Masculinities and Crime, edited
by Tim Newburn and Elizabeth A. Stanko. London: Routledge.
Greenberg, David F. 1977. “Delinquency and the Age Structure of Society.” Contemporary Crisis 1:189-223.
⎯⎯⎯. 1985. “Age, Crime and Social Explanation.” American Journal of Sociology 91:1-21.
⎯⎯⎯. 2001. “Time Series Analysis of Crime Rates.” Journal of Quantitative Criminology 17
(4): 291-327.
Grogger, Jeffrey. 1998. “Market Wages and Youth Crime.” Journal of Labor Economics 16:75691.
⎯⎯⎯. 2000. “An Economic Model of Recent Trends in Violence.” In The Crime Drop in America, edited by Alfred Blumstein and Joel Wallman. Cambridge, UK: Cambridge University
Press.
258 Journal of Research in Crime and Delinquency
Hamilton, Lawrence C. 1992. Regression with Graphics. Belmont, CA: Duxbury Press.
Hetherington, E. Mavis, Martha Cox, and Roger Cox. 1978. “The Aftermath of Divorce.” Pp.
148-76 in Mother-Child, Father-Child Relations, edited by Joseph H. Stevens and Marilyn
Mathews. Washington, DC: National Association for the Education of Young Children
Press.
Hirschi, Travis. 1969. Causes of Delinquency. University of California Press: Berkeley, CA.
Hirschi, Travis and Michael Gottfredson. 1983. “Age and the Explanation of Crime.” American
Journal of Sociology 89:552-84.
Hsiao, Cheng. 2003. Analysis of Panel Data. Cambridge, UK: Cambridge University Press.
Johnston, Jack and John DiNardo. 1997. Econometric Methods. New York: McGraw-Hill.
Kahn, Joan A. and William M. Mason. 1987. “Political Alienation, Cohort Size, and the
Easterlin Hypothesis.” American Sociological Review 52:155-69.
Land, Kenneth C., Patricia L. McCall, and Lawrence E. Cohen. 1990. “Structural Covariates of
Homicide Rates: Are There Any Invariances Across Time and Social Space?” American
Journal of Sociology 95:922–63.
Land, Kenneth C., David Cantor, and Stephen T. Russell. 1995 “Unemployment and Crime Rate
Fluctuations in the Post-World War II United States: Statistical Time Series Properties and
Alternative Models.” Pp. 55-79 in Crime and Inequality, edited by John Hagan and Ruth D.
Peterson. Stanford, CA: Stanford University Press.
Levin, Andrew, Chien-Fu Lin, and Chia-Shang James Chu. 2002. “Unit Root Tests in Panel
Data: Asymptotic and Finite-Sample Properties.” Journal of Econometrics 108:1-24.
Levitt, Steven. 1996. “The Effect of Prison Population Size on Crime Rates: Evidence from
Prison Overcrowding Litigation.” Quarterly Journal of Economics 11:319-52.
⎯⎯⎯. 2001. “Alternative Strategies for Identifying the Link between Unemployment and
Crime.” Journal of Quantitative Criminology 17 (4): 377-90.
Liedka, Raymond V., Anne Morrison Piehl, and Bert Useem. 2001. “The Crime-Control Effect
of Incarceration: Reconsidering the Evidence.” Washington, DC: Final Report to the
National Institute of Justice.
Lott, John R. 1998. More Guns, Less Crime: Understanding Crime and Gun-Control Laws. Chicago: University of Chicago Press.
Marvell, Thomas B. and Carlisle E. Moody, Jr. 1991. “Age Structure and Crime Rates: The Conflicting Evidence.” Journal of Quantitative Criminology 7 (3): 237-73.
⎯⎯⎯. 1996. “Specification Problems, Police Levels, and Crime Rates.” Criminology 34 (4):
609-46.
Matza, David. 1964. Delinquency and Drift. New York: Wiley.
McLanahan, Sarah and Gary Sandefur. 1994. Growing Up with a Single Parent: What Hurts,
What Helps? Cambridge, MA: Harvard University Press.
Merton, Robert K. 1938. “Social Structure and Anomie.” American Sociological Review 3:672-82.
Messerschmidt, James W. 1993. Masculinities and Crime: Critique and Reconceptualization of
Theory. Lanham, MD: Rowman and Littlefield.
Murphy, K. M., M. Plant, and F. Welch. 1988. “Cohort Size and Earnings in the USA.” Pp. 39-58
in Economics of Changing Age Distributions in Developed Countries, edited by R. D. Lee,
W. B. Arthur, and G. Rodgers. Oxford: Clarendon.
O’Brien, Robert M. 1989. “Relative Cohort Size and Age-Specific Crime Rates: An AgePeriod-Relative-Cohort-Size Model.” Criminology 27:57-78.
O’Brien, Robert M. and Jean Stockard. 2002. “Variations in Age-Specific Homicide Death
Rates: A Cohort Explanation for Changes in the Age Distribution of Homicide Deaths.”
Social Science Research 31:124-50.
Phillips / U.S. Age Structure and Homicide Rates 259
O’Brien, Robert M., Jean Stockard, and Lynne Isaacson 1999. “The Enduring Effects of Cohort
Characteristics on Age-Specific Homicide Rates, 1960-1995.” American Journal of Sociology 104 (4): 1061-95.
O’Hare, William P. 1996. “A New Look at Poverty in America.” Population Bulletin 51 (2): 2-48.
Washington DC: Population Reference Bureau.
Pampel, Fred C. and Rosemary Gartner. 1995. “Age Structure, Socio-Political Institutions, and
National Homicide Rates.” European Sociological Review 11 (3): 243-60.
Pampel, Fred C. and Elizabeth Peters. 1995. “The Easterlin Effect.” Pp. 153-95 in Annual Review
of Sociology, Vol. 2, edited by John Hagan and Karen S. Cook. Palo Alto, CA: Annual
Review Press.
Parker, Karen F., Patricia L. McCall, and Kenneth C. Land. 1999. “Determining Social-Structural
Predictors of Homicide: Units of Analysis and Related Methodological Concerns.” Pp. 107124 in Homicide: A Sourcebook of Social Research, edited by M. Dwayne Smith and Margaret A. Zahn. Thousand Oaks, CA: Sage.
Phillips, Julie A. Forthcoming. “Explaining Discrepant Findings in Cross-Sectional and Longitudinal Analyses: An Application to U.S. Homicide Rates.” Social Science Research.
Reidel, Marc. 1999. “Sources of Homicide Data: A Review and Comparison.” In Homicide: A
Sourcebook of Social Research, edited by M. Dwayne Smith and Margaret A. Zahn. Thousand Oaks, CA: Sage.
Sagi, Philip C. and Charles F. Wellford. 1968. “Age Composition and Patterns of Change in
Criminal Statistics.” Journal of Criminal Law, Criminology, and Police Science 59:29-36.
Sampson, Robert J. 1987. “Urban Black Violence: The Effect of Male Joblessness and Family
Disruption.” American Journal of Sociology 93:348–82.
Sampson, Robert J. and William Julius Wilson. 1995. “Toward a Theory of Race, Crime, and
Urban Inequality.” Pp. 37-54 in Crime and Inequality, edited by John Hagan and Ruth D.
Peterson. Stanford, CA: Stanford University Press.
Savolainen, J. 2000. “Relative Cohort Size and Age-Specific Arrest Rates: A Conditional Interpretation of the Easterlin Effect.” Criminology 38:117-36.
Smith, J. P. and F. Welch. 1981. “No Time to be Young: The Economic Prospects for Large
Cohorts in the United States.” Population Development Review 7:71-83.
Steffensmeier, Darrell J., Emilie A. Allan, Miles D. Harer, and Cathy Streifel. 1989. “Age and
the Distribution of Crime.” American Journal of Sociology 94:803-31.
Steffensmeier, Darrell, and Miles Harer. 1987. “Is the Crime Rate Really Falling? An ‘Aging’
U.S. Population and Its Impact on the Nation’s Crime Rate, 1980-1984.” Journal of Research
in Crime and Delinquency 24 (1): 23-48.
Steffensmeier, Darrell J., Cathy Streifel, and Edward S. Shihadeh. 1992. “Cohort Size and Arrest
Rates over the Life Course: The Easterlin Hypothesis Reconsidered.” American Sociological
Review 57:306-14.
Tittle, Charles R. 1988. “Two Empirical Regularities (Maybe) in Search of an Explanation:
Commentary on the Age-Crime Debate.” Criminology 26 (1): 75-85.
U.S. Department of Commerce, Bureau of the Census. 1999. Intercensal Estimates of the Population of Counties by Age, Sex, and Race: 1970-1999 [United States]. ICPSR ed. Ann Arbor,
MI: Inter–university Consortium for Political and Social Research [producer and
distributor].
U.S. Department of Commerce, Bureau of Economic Analysis. 2000. Regional Economic Information System: 1969–2000. Geospatial & Statistical Data Center Website.
U.S. Department of Commerce, Bureau of Labor Statistics. 1967–1999. Consumer Price Index–
All Urban Consumers. 1967–1999. Bureau of Labor Statistics Website.
260 Journal of Research in Crime and Delinquency
U.S. Department of Health and Human Services, National Center for Health Statistics. 1999.
Mortality Detail Files, 1968–1999 [Computer file]. Hyattsville, MD: U.S. Dept. of Health
and Human Services, National Center for Health Statistics [producer], 1999. Ann Arbor, MI:
Inter–university Consortium for Political and Social Research [distributor].
Wirth, Louis. 1969. “Urbanism as a Way of Life.” Pp. 67-83 in Classic Essays on the Culture of
Cities, edited by Richard Sennett. New York: Appleton-Century-Crofts.
Wooldridge, Jeffrey M. 2002. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: The MIT Press.
Worrall, John L. and Travis C. Pratt. 2004. “Estimation Issues Associated with Time-Series—
Cross-Section Analysis in Criminology.” Western Criminology Review 5(1):35-49.
Julie A. Phillips is an assistant professor in the Department of Sociology and affiliate of the
Institute for Health, Health Care Policy and Aging Research at Rutgers University. In addition to
her work on temporal and spatial patterns in homicide, she also studies reasons for racial and ethnic differences in homicide rates and marital disruption.