IDEAS home Printed from https://ideas.repec.org/a/dem/demres/v45y2021i16.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.demographic-research.org/volumes/vol45/16/45-16.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.4054/DemRes.2021.45.16?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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.
    3. 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.
    4. 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.
    5. Robert Mare, 2011. "A Multigenerational View of Inequality," Demography, Springer;Population Association of America (PAA), vol. 48(1), pages 1-23, February.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Hal Caswell & Rachel Margolis & Ashton Verdery, 2023. "The formal demography of kinship V: Kin loss, bereavement, and causes of death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 49(41), pages 1163-1200.
    3. Margherita Moretti & Elisa Cisotto & Alessandra De Rose, 2024. "Uncovering disability-free grandparenthood in Italy between 1998 and 2016 using gender-specific decomposition," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 50(42), pages 1247-1264.
    4. 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.
    5. Hal Caswell, 2024. "The formal demography of kinship VI: Demographic stochasticity and variance in the kinship network," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 51(39), pages 1201-1256.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hal Caswell & Rachel Margolis & Ashton Verdery, 2023. "The formal demography of kinship V: Kin loss, bereavement, and causes of death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 49(41), pages 1163-1200.
    2. Sha Jiang & Wenyun Zuo & Zhen Guo & Hal Caswell & Shripad Tuljapurkar, 2023. "How does the demographic transition affect kinship networks?," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 48(32), pages 899-930.
    3. Robert D. Mare, 2015. "Measuring Networks beyond the Origin Family," The ANNALS of the American Academy of Political and Social Science, , vol. 657(1), pages 97-107, January.
    4. 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.
    5. Paula Fomby & Laurie James-Hawkins & Stefanie Mollborn, 2015. "Family Resources in Two Generations and School Readiness Among Children of Teen Parents," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 34(5), pages 733-759, October.
    6. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    7. Xi Song & Robert D. Mare, 2019. "Shared Lifetimes, Multigenerational Exposure, and Educational Mobility," Demography, Springer;Population Association of America (PAA), vol. 56(3), pages 891-916, June.
    8. 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.
    9. Hal Caswell, 2024. "The formal demography of kinship VI: Demographic stochasticity and variance in the kinship network," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 51(39), pages 1201-1256.
    10. Ashton M. Verdery, 2015. "Links Between Demographic and Kinship Transitions," Population and Development Review, The Population Council, Inc., vol. 41(3), pages 465-484, September.
    11. Thomas Leopold & Charlotte Clara Becker & Zafer Buyukkececi & Beyda Çineli & Marcel Raab, 2024. "KINMATRIX: A new data resource for studies of families and kinship," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 51(25), pages 789-808.
    12. Jane Menken, 1985. "Age and fertility: How late can you wait?," Demography, Springer;Population Association of America (PAA), vol. 22(4), pages 469-483, November.
    13. Sirois, Catherine, 2020. "The strain of sons' incarceration on mothers’ health," Social Science & Medicine, Elsevier, vol. 264(C).
    14. Michelle Maroto, 2018. "Saving, Sharing, or Spending? The Wealth Consequences of Raising Children," Demography, Springer;Population Association of America (PAA), vol. 55(6), pages 2257-2282, December.
    15. Kieron Barclay & Torkild Lyngstad & Dalton Conley, 2018. "The Production of Inequalities within Families and Across Generations: The Intergenerational Effects of Birth Order and Family Size on Educational Attainment," NBER Working Papers 24530, National Bureau of Economic Research, Inc.
    16. John Robert Warren, 2015. "Potential Data Sources for a New Study of Social Mobility in the United States," The ANNALS of the American Academy of Political and Social Science, , vol. 657(1), pages 208-246, January.
    17. van den Berg, Gerard J. & Pinger, Pia R., 2016. "Transgenerational effects of childhood conditions on third generation health and education outcomes," Economics & Human Biology, Elsevier, vol. 23(C), pages 103-120.
    18. Kroeger, Sarah & Thompson, Owen, 2016. "Educational mobility across three generations of American women," Economics of Education Review, Elsevier, vol. 53(C), pages 72-86.
    19. Michael Hout, 2015. "A Summary of What We Know about Social Mobility," The ANNALS of the American Academy of Political and Social Science, , vol. 657(1), pages 27-36, January.
    20. Diego Alburez-Gutierrez, 2021. "The demographic drivers of grief and memory after genocide in Guatemala," MPIDR Working Papers WP-2021-003, Max Planck Institute for Demographic Research, Rostock, Germany.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:dem:demres:v:45:y:2021:i:16. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Editorial Office (email available below). General contact details of provider: https://www.demogr.mpg.de/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.