The Cross-Classified Age-Period-Cohort Model as a Constrained Estimator

Liying Luo, University of Minnesota
James Hodges, University of Minnesota

In many different fields, researchers desire to separate age, period, and cohort effects. Among methods proposed to address the identification problem in Age-Period-Cohort analysis, the cross-classified approach, including Cross-Classified Fixed Effects Models (CCFEM) and Cross-Classified Random Effects Models (CCREM), appear to solve the identification problem and to yield good estimates of the true APC effects. This paper assesses the validity and application scope of CCFEM and CCREM theoretically and illustrates their properties with simulations. It shows that the cross-classified methods do not automatically solve the identification problem; rather, they address this problem by implicitly imposing multiple constraints on the coefficient vector. These constraints not only depend on the width of the APC intervals but also have non-trivial implications for estimation. Because these constraints are extremely difficult to verify, the authors conclude that CCFEM and CCREM cannot and should not be used to recover the true age, period, and cohort effects.