period, and cohorts accounts for part (about half) of this upward shift in youth homicide, but not all of it.
Of course, when we add the dummy variables for those 15-19 and 20-24 in 1990 and 1995 they account
for all of this variance (they fit the observed data perfectly for these two age groups in these two periods).
Our statistical test presented earlier show that this improvement in fit is statistically significant (not likely
just a chance fluctuation). This is a clear indication that even though the cohort thesis suggests higher
rates for the 15-to-19 year olds in both 1990 and 1995 than the invariant age curve, the upward shift in
homicide rates for that group were greater than can be accounted for by cohort replacement. By the year
2000 the cohort replacement model is quite consistent with the observed age curve and the “invariant”
age curve does not fit well at both the youngest and oldest age levels.
Discussion
The basic analyses in this paper examine mechanisms that summarize descriptively what has happened to
the age distribution of homicide offenses over the relatively recent past in the United States. On average
there is a general, relatively stable age curve with a peak at the 20-to-24 age group and a decline
thereafter. This pattern in terms of the peak age group for homicide offenses fits the observed rates for all
of the periods we investigated (1965, 1970, . . ., 2005) except for 1990 and 1995. There is a relative
stable and important relationship between age and homicide rates over this period.
Important shifts in this age curve have occurred throughout the period 1965 – 2005 that are
related to cohort replacement (we measure cohort effects as enduring throughout the lifespan of the
cohort). Figures 2 and 3 show the importance of cohort replacement: models containing age, period, and
cohort dummy variables fit the observed age curve substantially better than those that contain only age
and period. The impact of cohort replacement is also reflected in the statistically significant increase in
the sums of squares accounted for in the age-period-specific rates when the cohort dummy variables are
entered into models that control for age and period effects.
While cohort replacement is associated with some of the upturn in the homicide offending of
youth during 1990 and 1995, it does not account for all of this upturn. From the graphs, it accounts for
about half of this upturn, but it depends on which of these two periods we consider. There is certainly a
strong deviation from the cohort replacement model during the two periods of the epidemic of youth
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Convention