Identification of Parameters in Cohort Models

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Abstract
Linear-additive age-period cohort models that permit the maximum number of aging effects, period effects, and cohort effects (full cohort models) are underidentified. In this article, some general rules will be given for detecting identified and underidentified parameters in any full cohort model under zero-sum restrictions. It will be demonstrated that only one parameter in a dimension is identified whenever the number of parameters in this dimension is uneven. Otherwise, no parameter is identified. Full cohort models for larger tables contain more overidentifying restrictions, but the number of identified parameters never exceeds four. Furthermore, it will be shown which additional parameter restrictions are sufficient and which are inappropriate for the identification of all parameters in a model.