The Cohort-Size Sample-Size Conundrum: An Empirical Analysis and Assessment Using Homicide Arrest Data from 1960 to 1999

A number of studies use the Age-Period-Cohort Characteristic (APCC) model to address the impact of cohort related factors on the age distribution of homicide offending. Several of these studies treat birth cohorts as spanning several years, an operationalization that most closely matches tenets of cohort theory, yet sharply reduces the number of observations available for analysis. Other studies define birth cohorts as those born within a single year, an operationalization that is theoretically problematic, but provides many more observations for analysis. We address the sample size problem by applying a time-series-cross-section model (panel model) with age-period-specific homicide arrest data from the United States for each year from 1960 to 1999, while operationalizing cohorts as five-year birth cohorts. Our panel model produces results that are very similar to those obtained from traditional multiyear APCC models. Substantively, the results provide a replication of work showing the importance of relative cohort size and cohort variations in family structure for explaining variations in age-period-specific homicide rates. The additional observations provided by our approach allow us to examine these relationships over time, and we find substantively important changes. The year-by-year estimates of the age distribution of homicide offending help us to examine the model during the epidemic of youth homicide.