Preprint

Vertical kinship distribution at the population level: a Mamushka approximation

Williams, I., Alburez-Gutierrez, D.

SocArXiv papers
54 pages.
SocArXiv
submitted: 09 September 2026 / last edited: 10 September 2026 (version 1) (2026), unpublished

DOI:10.31235/osf.io/j36st_v1

Open Access

Reproducible

Abstract

Understanding the population-level distribution of parents, grandparents, and great-grandparents is increasingly important as fertility declines and kin networks thin. However, standard kinship demography tools do not easily capture these distributions when vertical kin are shared across individuals. We introduce a simple approximation to estimate age-specific proportions of women who are childless, mothers, grandmothers, and great-grandmothers from period fertility and mortality schedules. The approach relies on conditional first-order fertility hazards combined with standard age-specific fertility and survival rates, assuming a time-invariant regime and an age-specific distribution of parity. We illustrate the method using Argentine census data and vital statistics, and assess its performance by comparison with a demographic microsimulation. Results show pronounced declines over time in the prevalence of higher-order generational roles, alongside strong subnational heterogeneity. These findings demonstrate how declining fertility reshapes vertical kin availability and provide a tractable tool for studying kinlessness and intergenerational support in population ageing contexts. A key Further development can formally account for heterogeneity across multiple dimensions.