# Variation in Vital Rates by Age, Period, and Cohort

**Citation:** *Wilmoth, John R. Variation in Vital Rates by Age, Period, and Cohort. Sociological Methodology (RSS)*

**Tagged:** uw-madison (RSS), wisconsin (RSS), sociology (RSS), demography (RSS), prelim (RSS), qual (RSS), WisconsinDemographyPrelimAugust2009 (RSS)

**Summary:**

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. A complete, symmetric decomposition of the data array into age, period, and cohort components is not attempted. Instead, 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 2 directions. This 2-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. This is an icky paper that I basically did not understand that attempts to decompose mathematically large arrays of age-specific mortality rates into separate age, period, and cohort components. Sorry I am not more helpful. Feel free to read it and explain it to me!