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The formal demography of kinship III: Kinship dynamics with time-varying demographic rates

Author

Listed:
  • Hal Caswell

    (Universiteit van Amsterdam)

  • Xi Song

    (University of Pennsylvania)

Abstract

Background: Kinship models, from the pioneering work of Goodman, Keyfitz, and Pullum to the recent matrix-oriented approach of Caswell, have assumed time-invariant demographic rates, and computed the kinship structures implied by those rates. In reality, however, demographic rates vary with time and it is of interest to compute the consequences of such variation for kinship structures. Objective: Our goal is to develop a matrix model for the dynamics of kinship networks subject to arbitrary temporal variation in survival, fertility, and population structure. Methods: We develop a linked set of equations for the dynamics of the age structure of each type of kin of a Focal individual. The matrices that describe survival and fertility are given as functions of time. The initial conditions required for the time-invariant model are replaced with a set of boundary conditions for initial time and initial age. Results: The time-varying model maintains the kinship network structure of the time-invariant model. In addition to the results provided by the time-invariant model, it provides kinship structures by period, cohort, and age. It applies equally to historical sequences of past demographic rates and to projections of future rates. As an illustration, we present an analysis of the kinship structure of Sweden from 1891 to 2120. Contribution: The time-varying kinship model makes it possible to analyze the consequences of changing demographic rates, in the past or the future. It is easily computable, requires no simulations, and is readily extended to include additional, more distant relatives in the kinship network. The method can also be used to show the growth of families, lineages, and dynasties in populations across time and place and between social groups.

Suggested Citation

  • Hal Caswell & Xi Song, 2021. "The formal demography of kinship III: Kinship dynamics with time-varying demographic rates," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 45(16), pages 517-546.
    • Handle: RePEc:dem:demres:v:45:y:2021:i:16
    DOI: 10.4054/DemRes.2021.45.16
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    References listed on IDEAS

    as
    1. Judith A. Seltzer, 2019. "Family Change and Changing Family Demography," Demography, Springer;Population Association of America (PAA), vol. 56(2), pages 405-426, April.
    2. Hal Caswell, 2020. "The formal demography of kinship II: Multistate models, parity, and sibship," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 42(38), pages 1097-1146.
    3. Robert Mare, 2011. "A Multigenerational View of Inequality," Demography, Springer;Population Association of America (PAA), vol. 48(1), pages 1-23, February.
    4. Thomas Pullum, 1982. "The Eventual Frequencies of Kin in a Stable Population," Demography, Springer;Population Association of America (PAA), vol. 19(4), pages 549-565, November.
    5. Hal Caswell, 2008. "Perturbation analysis of nonlinear matrix population models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 18(3), pages 59-116.
    6. Peter Uhlenberg, 2009. "Children in an Aging Society," The Journals of Gerontology: Series B, The Gerontological Society of America, vol. 64(4), pages 489-496.
    7. Hal Caswell, 2019. "The formal demography of kinship: A matrix formulation," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(24), pages 679-712.
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    Cited by:

    1. Hal Caswell, 2022. "The formal demography of kinship IV: Two-sex models and their approximations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 47(13), pages 359-396.
    2. Diego Alburez-Gutierrez & Ugofilippo Basellini & Emilio Zagheni, 2022. "When do parents bury a child? Quantifying uncertainty in the parental age at offspring loss," MPIDR Working Papers WP-2022-016, Max Planck Institute for Demographic Research, Rostock, Germany.

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    More about this item

    Keywords

    kinship; family; population projection; matrix population models; Sweden;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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