Estimable intra-age, intra-period, and intra-cohort effects in age-period-cohort multiple classification models

Abstract

Even if a researcher found a constraint that correctly identified an age-period-cohort multiple classification (APCMC) model, the results would not address the issue of how stable these effects are within ages, periods, or cohorts. This occurs because APCMC models are based on the main effects for each age group, each period, and each cohort, and these main effects only assess the additive effects of ages, periods, and cohorts. The main effects of ages are constant across periods and cohorts, the main effects of periods are constant across ages and cohorts, and the main effects of cohorts are constant across ages and periods. I present a method for assessing the stability of age effects within ages, period effects within periods, and cohort effects within cohorts. For example, does the cohort effect for a specific cohort diminish as the cohort ages or is it enhanced; is the period effect for a particular period stronger for younger aged people than for older aged people or does only a single age-group in a particular period deviate from the trend within that period. The proposed measures of the stability of these effects are based on estimable functions from the full APCMC model. Such functions are the same no matter which just identifying constraint is applied to the APCMC model. I illustrate the use of this approach using homicide arrest data for the United States from 1965 to 2015.