MPIDR Working Paper

A unified framework of demographic time

Riffe, T., Schöley, J., Villavicencio, F.
MPIDR Working Paper WP-2015-008, 22 pages.
Rostock, Max-Planck-Institut für demografische Forschung (November 2015)
Revised October 2016 Please refer to the peer-reviewed version, published Aug 22, 2017 in Genus DOI: The published version has been substantially revised from the last WP version.
Open Access


Demographic thought and practice is largely conditioned by the Lexis diagram, a two-dimensional graphical representation of the identity between age, period, and birth cohort. This relationship does not account for remaining years of life or other related time measures, whose use in demographic research is both underrepresented and incompletely situated. We describe a three-dimensional relationship between six different measures of demographic time: chronological age, time to death, lifespan, time of birth, time of death, and period. We describe four identities among subsets of these six measures, and a full identity that relates the six of them. One of these identities is the age-period-cohort identity, while the other three are relatively novel. We provide a topological overview of the diagrams that pertain to these identities. The 3-d geometric representation of the full six-way identity is proposed as a coordinate system that fully describes temporal variation in demographic data. We offer this framework as an instrument to enable the discovery of yet-undescribed relationships and patterns in formal and empirical demography.

Schlagwörter: demography
Das Max-Planck-Institut für demografische Forschung (MPIDR) in Rostock ist eines der international führenden Zentren für Bevölkerungswissenschaft. Es gehört zur Max-Planck-Gesellschaft, einer der weltweit renommiertesten Forschungsgemeinschaften.