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Working Paper

Date of this Version



If you know when someone was born, and you know what time it is, you know how old they are. If you know how old someone is and when they were born, you know the date on which they are being observed. If you know someone’s age as of a given time, you know when they were born. These are ineluctable features of algebra (age ≡ period – cohort) and geometry, as reflected in the Lexis diagram (Chauvel 2014, 384-389). There are many ways that one can turn the problem (e.g., cohort ≡ period – age) and thus many alternative forms of observation, classification, and depiction. However, there is a strong statistical sense in which there are only two pieces of information, not three.


Paper prepared for the volume Age, Period and Cohort Effects: The Identification Problem, and What to Do about It, edited by Andrew Bell. Routledge. Version of 30 May 2020. Thanks to Theodore Holford for a helpful reading, and to Tomáš Sobotka for his generosity in providing the data and graphics that appear here as Figures 4 and 5.


age, cohort analysis, age-period-cohort model



Date Posted: 01 June 2020