IDEAS home Printed from https://ideas.repec.org/a/dem/demres/v49y2023i26.html

Variable-r in sex ratios: Formulas in honor of Jim Vaupel

Author

Listed:
  • Vladimir Canudas-Romo

    (Australian National University)

  • Wen Su

    (University of Oxford)

  • Mike Hollingshaus

    (University of Utah)

Abstract

Background: Two seminal studies in the 1980s, by Preston and Coale (1982) and Arthur and Vaupel (1984), generalized the Lotka equations developing the variable-r methods. Objective: Time changes in sex ratios (males:females) are studied from the perspective of the variable-r method to estimate the contributions of fertility, mortality, and net-migration. Methods: The time change in sex ratios can be calculated as a comparison of the growth rates of the sexes. The difference is then decomposed into population composition, and the age-specific components of fertility, mortality, and net migration. Thirteen countries with long historical demographic series are used to illustrate the time trends in sex ratios. Results: Most countries are moving towards a greater number of males per females. The greatest changes were observed in Norway and Sweden, with males catching up with females at older ages due to survival. Meanwhile, the sex differential in net-migration flows explains the decline in sex ratios in Spain and Australia and the increase in the United States. Conclusions: Our results shed light on the debate on female–male population imbalances and how fertility, mortality, and net migration contribute to these disparities. Contribution: Vaupel and Canudas-Romo (2003) wrote a paper in honor of Vaupel’s mentor Nathan Keyfitz on his 90th anniversary. The paper focused on a common topic of interest of all three researchers, namely mathematical demography. In honor of the legacy of the work of Jim Vaupel, we revive that idea with a collection of mathematical derivations that are simple, yet powerful in their demographic interpretation.

Suggested Citation

  • Vladimir Canudas-Romo & Wen Su & Mike Hollingshaus, 2023. "Variable-r in sex ratios: Formulas in honor of Jim Vaupel," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 49(26), pages 693-722.
    • Handle: RePEc:dem:demres:v:49:y:2023:i:26
    DOI: 10.4054/DemRes.2023.49.26
    as

    Download full text from publisher

    File URL: https://www.demographic-research.org/volumes/vol49/26/49-26.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.4054/DemRes.2023.49.26?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. Mike Hollingshaus & Rebecca Utz & Ryan Schacht & Ken R. Smith, 2019. "Sex ratios and life tables: Historical demography of the age at which women outnumber men in seven countries, 1850–2016," Historical Methods: A Journal of Quantitative and Interdisciplinary History, Taylor & Francis Journals, vol. 52(4), pages 244-253, October.
    2. James W. Vaupel & Vladimir Canudas-Romo, 2002. "Decomposing demographic change into direct vs. compositional components," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 7(1), pages 1-14.
    3. Marc Luy, 2003. "Causes of Male Excess Mortality: Insights from Cloistered Populations," Population and Development Review, The Population Council, Inc., vol. 29(4), pages 647-676, December.
    4. Stuart Basten & Georgia Verropoulou, 2013. "'Maternity migration' and the increased sex ratio at birth in Hong Kong SAR," Population Studies, Taylor & Francis Journals, vol. 67(3), pages 323-334, November.
    5. Samuel Preston & Christine Himes & Mitchell Eggers, 1989. "Demographic Conditions Responsible for Population Aging," Demography, Springer;Population Association of America (PAA), vol. 26(4), pages 691-704, November.
    6. James Vaupel & Vladimir Romo, 2003. "Decomposing change in life expectancy: A bouquet of formulas in honor of Nathan Keyfitz’s 90th birthday," Demography, Springer;Population Association of America (PAA), vol. 40(2), pages 201-216, May.
    7. Samuel H. Preston & Andrew Stokes, 2012. "Sources of Population Aging in More and Less Developed Countries," Population and Development Review, The Population Council, Inc., vol. 38(2), pages 221-236, June.
    8. Michael Murphy, 2017. "Demographic Determinants of Population Aging in Europe since 1850," Population and Development Review, The Population Council, Inc., vol. 43(2), pages 257-283, June.
    9. Shiro Horiuchi & Samuel Preston, 1988. "Age-specific growth rates: The legacy of past population dynamics," Demography, Springer;Population Association of America (PAA), vol. 25(3), pages 429-441, August.
    10. Josh Angrist, 2002. "How Do Sex Ratios Affect Marriage and Labor Markets? Evidence from America's Second Generation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 997-1038.
    11. Frank Bean & Allan King & Jeffrey Passel, 1983. "The number of illegal migrants of Mexican origin in the United States: Sex ratio-based estimates for 1980," Demography, Springer;Population Association of America (PAA), vol. 20(1), pages 99-109, February.
    12. James Raymer & Yanlin Shi & Qing Guan & Bernard Baffour & Tom Wilson, 2018. "The Sources and Diversity of Immigrant Population Change in Australia, 1981–2011," Demography, Springer;Population Association of America (PAA), vol. 55(5), pages 1777-1802, October.
    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. Henrik-Alexander Schubert & Christian Dudel, 2025. "Subnational birth squeezes: male-female TFR differences across eight high- and middle-income countries over time," MPIDR Working Papers WP-2025-025, Max Planck Institute for Demographic Research, Rostock, Germany.

    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. Vladimir Canudas-Romo & Tianyu Shen & Collin Payne, 2021. "The role of reductions in old-age mortality in old-age population growth," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 44(44), pages 1073-1084.
    2. Henseke, Golo & Tivig, Thusnelda, 2013. "Alterung in Berufen: Der Beitrag ökonomischer Einflüsse," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 80001, Verein für Socialpolitik / German Economic Association.
    3. Kim, Hyun Kyung & Lee, Sang-Hyop, 2021. "The effects of population aging on South Korea’s economy: The National Transfer Accounts approach," The Journal of the Economics of Ageing, Elsevier, vol. 20(C).
    4. Fernando Fernandes & Cássio M. Turra & Eduardo L.G. Rios Neto, 2023. "World population aging as a function of period demographic conditions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 48(13), pages 353-372.
    5. Wen Su & Alyson van Raalte & José Manuel Aburto & Vladimir Canudas-Romo, 2024. "Subnational contribution to life expectancy and life span variation changes: Evidence from the United States," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 50(22), pages 583-624.
    6. Michael Murphy, 2021. "Use of Counterfactual Population Projections for Assessing the Demographic Determinants of Population Ageing," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 211-242, March.
    7. Roland Rau & Gabriele Doblhammer & Vladimir Canudas-Romo & Zhang Zhen, 2008. "Cause-of-Death Contributions to Educational Inequalities in Mortality in Austria between 1981/1982 and 1991/1992," European Journal of Population, Springer;European Association for Population Studies, vol. 24(3), pages 265-286, September.
    8. Glenn Firebaugh & Francesco Acciai & Aggie Noah & Christopher J Prather & Claudia Nau, 2014. "Why the racial gap in life expectancy is declining in the United States," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(32), pages 975-1006.
    9. Eugenio Paglino, 2026. "The groupwise decomposition: Estimating group-specific contributions to differences between demographic measures," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 54(14), pages 441-470.
    10. Samuel H. Preston & Yana C. Vierboom, 2021. "The Changing Age Distribution of the United States," Population and Development Review, The Population Council, Inc., vol. 47(2), pages 527-539, June.
    11. Agnieszka Fihel & Anna Janicka & Weronika Kloc-Nowak, 2018. "The direct and indirect impact of international migration on the population ageing process: A formal analysis and its application to Poland," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 38(43), pages 1303-1338.
    12. Qi Cui & Vladimir Canudas-Romo & Heather Booth, 2019. "The Mechanism Underlying Change in the Sex Gap in Life Expectancy at Birth: An Extended Decomposition," Demography, Springer;Population Association of America (PAA), vol. 56(6), pages 2307-2321, December.
    13. Vytenis Juozas Deimantas & A. Ebru Şanlıtürk & Leo Azzollini & Selin Köksal, 2024. "Population Dynamics and Policies in Europe: Analysis of Population Resilience at the Subnational and National Levels," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 43(2), pages 1-28, April.
    14. Audrey Ugarte & Onofre Alves Simões, 2020. "Breaking Life Expectancy into Small Pieces," Working Papers REM 2020/0154, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    15. Carl P. Schmertmann & T. J. Mathews & Charles B. Nam, 1994. "Demographic Influences On The Number Of Children At School Entry Ages, With Examples From Three States," The Review of Regional Studies, Southern Regional Science Association, vol. 24(2), pages 177-194, Fall.
    16. Markus Sauerberg & Marc Luy, 2024. "Standardized mean age at death (MADstd): Exploring its potentials as a measure of human longevity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 50(30), pages 871-898.
    17. Frank Trovato, 2005. "Narrowing Sex Differential in Life Expectancy in Canada and Austria: Comparative Analysis," Vienna Yearbook of Population Research, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna, vol. 3(1), pages 17-52.
    18. repec:plo:pone00:0160320 is not listed on IDEAS
    19. Kota Ogasawara & Mizuki Komura, 2022. "Consequences of war: Japan’s demographic transition and the marriage market," Journal of Population Economics, Springer;European Society for Population Economics, vol. 35(3), pages 1037-1069, July.
    20. Sascha O. Becker & Lukas Mergele & Ludger Woessmann, 2020. "The Separation and Reunification of Germany: Rethinking a Natural Experiment Interpretation of the Enduring Effects of Communism," Journal of Economic Perspectives, American Economic Association, vol. 34(2), pages 143-171, Spring.
    21. Tomasz Wrycza & Annette Baudisch, 2012. "How life expectancy varies with perturbations in age-specific mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 27(13), pages 365-376.

    More about this item

    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:49:y:2023:i:26. 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.