Setting bounds on age, period, and cohort effects using observed data

This paper presents a method that uses observed data from an age-period table to set bounds on the age, period, and cohort effects in an age-period-cohort multiple classification (APCMC) model. The rationale is that with enough periods over a long time span the age distributions within periods on the dependent variable will be affected by different sets of cohorts for each of the periods. This is likely to result in different trends in these separate period age distributions such that the trends in the age distributions will encompass the trend in the age effects that generated the dependent variable values. This approach can help to identify bounds that likely encompass the age, period, cohort parameters that generated the data. The data used in this papers are estimated homicide arrests by single years for those aged 15–64 for the periods 1964 to 2019 in the United States. I utilize the observed trends in the age-distributions for each of the 56 periods as different constraints on the trends for the age effects in the APCMC fixed effects model. These estimates are used to form bounds on the age effects, period effects, and cohort effects.