Volume 41 - Article 24 | Pages 679–712
The formal demography of kinship: A matrix formulation
By Hal Caswell
demographic-research.41-24 (zip file, 42 kB)
readme.41-24 (text file, 1 kB)
Abstract
Background: Any individual is surrounded by a network of kin that develops over her lifetime. In a justly famous paper, Goodman, Keyfitz, and Pullum (1974) presented formal calculations of the mean numbers of (female, matrilineal) kin implied by a mortality and fertility schedule.
Objective: The aim of this paper is a new theory of kinship demography that provides age distributions as well as expected numbers, permits calculation of properties (e.g., dependency) of kin, is easily computable, and does not require simulation.
Methods: The analysis relies on a novel application of the matrix formulation of cohort component population projection to describe the dynamics of a kinship network. The approach arises from the observation that the kin of a focal individual form a population, and can be modelled as one.
Results: Kinship dynamics are described by a coupled system of non-autonomous matrix equations. I show how to calculate age distributions, total numbers, prevalence, dependency, and the experience of the death of relatives. As an example, I compare the kinship networks implied by the period vital rates of Japanese women in 1947 and 2014. Over this interval, fertility declined by 70% while life expectancy increased by 60%. The implications of these changes for kinship structure are profound; a lifetime dominated, under 1947 rates, by the experience of the death of kin has changed to one in which the death of kin is a rare event. On the other hand, the burden of dependent aged kin, including those suffering from dementia, is many-fold larger under 2014 rates.
Contribution: This new theory opens to investigation hitherto inaccessible aspects of kinship, with potential applications to many problems in family demography.
Author's Affiliation
- Hal Caswell - Universiteit van Amsterdam, the Netherlands EMAIL
Other articles by the same author/authors in Demographic Research
The formal demography of kinship V: Kin loss, bereavement, and causes of death
Volume 49 - Article 41
The contributions of stochastic demography and social inequality to lifespan variability
Volume 49 - Article 13
How does the demographic transition affect kinship networks?
Volume 48 - Article 32
The formal demography of kinship IV: Two-sex models and their approximations
Volume 47 - Article 13
The formal demography of kinship III: Kinship dynamics with time-varying demographic rates
Volume 45 - Article 16
Healthy longevity from incidence-based models: More kinds of health than stars in the sky
Volume 45 - Article 13
The formal demography of kinship II: Multistate models, parity, and sibship
Volume 42 - Article 38
The sensitivity analysis of population projections
Volume 33 - Article 28
Lifetime reproduction and the second demographic transition: Stochasticity and individual variation
Volume 33 - Article 20
Demography and the statistics of lifetime economic transfers under individual stochasticity
Volume 32 - Article 19
A matrix approach to the statistics of longevity in heterogeneous frailty models
Volume 31 - Article 19
Why do lifespan variability trends for the young and old diverge? A perturbation analysis
Volume 30 - Article 48
Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates
Volume 23 - Article 19
Perturbation analysis of nonlinear matrix population models
Volume 18 - Article 3
Most recent similar articles in Demographic Research
KINMATRIX: A new data resource for studies of families and kinship
Volume 51 - Article 25
| Keywords:
family,
networks,
solidarity,
survey methodology,
transmission
Between money and intimacy: Brideprice, marriage, and women’s position in contemporary China
Volume 50 - Article 46
| Keywords:
brideprice,
China,
divorce,
family,
family law,
gender inequalities,
marriage
Pathways and obstacles to parenthood among women in same-sex couples in Spain
Volume 50 - Article 35
| Keywords:
assisted reproduction,
family,
fertility desires,
LGBTQ,
parenthood,
same-sex couples
Losing the female survival advantage: Sex differentials in infant and child mortality in Pakistan
Volume 50 - Article 15
| Keywords:
child mortality,
family,
gender discrimination,
Pakistan,
sex differentials,
son preference,
South Asia,
survival analysis
The formal demography of kinship V: Kin loss, bereavement, and causes of death
Volume 49 - Article 41
| Keywords:
bereavement,
causes of death,
competing risks,
kin loss,
kinship,
matrix models
Cited References: 51
Download to Citation Manager
PubMed
Google Scholar