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Title: Bounding Analyses of Age-Period-Cohort Models
Abstract:
For at least 80 years researchers in a wide variety of fields have sought to uniquely identify age, period, and cohort (APC) effects, even though an infinite number of solutions exist due to perfect linear dependency. In this paper we introduce a new approach for identifying APC effects based on bounding feasible regions of the parameter space. Depending on the location of the solution line in the parameter space, minimal constraints on the direction and magnitude of the linear trends can lead to substantively meaningful conclusions. Furthermore, bounds can be derived from mechanism-based modelsthat specify the processes by which one or more of the linear effects affect the outcome of interest, even when such models are misspecified. Unlike previous methods, our approach is based on applying theoretically-relevant and empirically-derived constraints only on those components of the APC effectsthat are unidentified. To illustrate the usefulness of bounding analyses of APC effects, we examine trends in verbal ability and perceived well-being. In contrast to previous research, we find strong overall effects for period and cohort forboth outcomes. We conclude with a discussion of Bayesian interpretations ofbounding analyses as well as guidelines for further research on APC effects.
