Homicide Arrest Rate Trends in the United States: The Contributions of Periods and Cohorts (1965–2015)

Abstract

To determine the contributions of period effects (controlling for ages and cohorts) and cohort effects (controlling for ages and periods) to the changes in the homicide arrest rates in the United States over the time span from 1965 to 2015. This determination faces the age–period–cohort identification problem: the linear trends of these three factors are linearly dependent and there are an infinite number of solutions that fit the data equally well. I address this problem in multiple ways: by setting reasonable bounds around the age-distribution of homicide arrests using constrained estimates, presenting estimable functions that are identified, and by using an age–period–cohort–characteristic model. The cohort effects on homicide arrest rates have on average trended upward since the cohort born in 1945–1949; and the period coefficients have on average trended downward since 1965, but trended upward during the mid-1960s to the early-1970s. These trends over time are somewhat different depending on the bounds under consideration. Theories that posit period effects as responsible for at least part of the drop in homicide rates from 1990 to 2015 and the increase in homicide rates from the mid-1960s to the early-1970 are consistent with this analysis. Cohort effects worked in the opposite direction of the period effects for the years from 1990 to 2015. The existence of both sets of effects has implications for criminological theories and for policy prescriptions.