Variation in vital rates by age, period, and cohort

"The analysis of age-specific vital rates is studied, and special attention is given to the problem of decomposing an array of rates into factors related to age, period, and cohort.... The paper focuses on the age and period dimensions and derives an initial description of the matrix's structure with regard to changes only in those two directions. This two-dimensional description is then augmented by a consideration of residual patterns that seem clearly linked to cohorts. The use of a model that is asymmetric in age, period, and cohort is justified by a detailed discussion of the problems of identification in models involving perfectly collinear independent variables. An important conclusion is that traditional modeling approaches that treat age, period, and cohort in a symmetric fashion are fundamentally flawed." Some of these concepts are illustrated using mortality data from France. This is a revised version of a paper originally presented at the 1989 Annual Meeting of the Population Association of America (see Population Index, Vol. 55, No. 3, Fall 1989, pp. 375-6).