A Mixed Model Estimation of Age, Period, and Cohort Effects

Abstract

For more than 30 years, sociologists and demographers have struggled to come to terms with the age, period, cohort conundrum: Given the linear dependency between age groups, periods, and cohorts, how can these effects be estimated separately? This article offers a partial solution to this problem. The authors treat cohort effects as random effects and age and period effects as fixed effects in a mixed model. Using this approach, they can (1) assess the amount of variance in the dependent variable that is associated with cohorts while controlling for the age and period dummy variables, (2) model the dependencies that result from the age-period-specific rates for a single cohort being observed multiple times, and (3) assess how much of the variance in observations that is associated with cohorts is explained by differences in the characteristics of cohorts. The authors use empirical data to see how their results compare with other analyses in the literature.