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Intrinsically dynamic population models

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  • Robert Schoen

    (Pennsylvania State University)

Abstract

Intrinsically dynamic models (IDMs) depict populations whose cumulative growth rate over a number of intervals equals the product of the long term growth rates (that is the dominant roots or dominant eigenvalues) associated with each of those intervals. Here the focus is on the birth trajectory produced by a sequence of population projection (Leslie) matrices. The elements of a Leslie matrix are represented as straightforward functions of the roots of the matrix, and new relationships are presented linking the roots of a matrix to its Net Reproduction Rate and stable mean age of childbearing. Incorporating mortality changes in the rates of reproduction yields an IDM when the subordinate roots are held constant over time. In IDMs, the birth trajectory generated by any specified sequence of Leslie matrices can be found analytically. In the Leslie model with 15 year age groups, the constant subordinate root assumption leads to reasonable changes in the age pattern of fertility, and equations (27) and (30) provide the population size and structure that result from changing levels of net reproduction. IDMs generalize the fixed rate stable population model. They can characterize any observed population, and can provide new insights into dynamic demographic behavior, including the momentum associated with gradual or irregular paths to zero growth.

Suggested Citation

  • Robert Schoen, 2005. "Intrinsically dynamic population models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 12(3), pages 51-76.
    • Handle: RePEc:dem:demres:v:12:y:2005:i:3
    DOI: 10.4054/DemRes.2005.12.3
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    References listed on IDEAS

    as
    1. Robert Schoen & Stefan Jonsson, 2003. "Modeling momentum in gradual demographic," Demography, Springer;Population Association of America (PAA), vol. 40(4), pages 621-635, November.
    2. Joshua Goldstein, 2002. "Population momentum for gradual demographic transitions: an alternative approach," Demography, Springer;Population Association of America (PAA), vol. 39(1), pages 65-73, February.
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    5. Robert Schoen, 2003. "Dynamic populations with uniform natural increase across states," Mathematical Population Studies, Taylor & Francis Journals, vol. 10(3), pages 195-210.
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    7. Ronald Lee, 1974. "The formal dynamics of controlled populations and the echo, the boom and the bust," Demography, Springer;Population Association of America (PAA), vol. 11(4), pages 563-585, November.
    8. Young Kim & Robert Schoen, 1996. "Populations with quadratic exponential growth," Mathematical Population Studies, Taylor & Francis Journals, vol. 6(1), pages 19-33.
    9. John Bongaarts & Rodolfo A. Bulatao, 1999. "Completing the Demographic Transition," Population and Development Review, The Population Council, Inc., vol. 25(3), pages 515-529, September.
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    Cited by:

    1. Robert Schoen & Claudia Nau, 2009. "Intrinsically Dynamic Multistate Models," Mathematical Population Studies, Taylor & Francis Journals, vol. 16(4), pages 231-247.
    2. Jan Beyersmann & Hein Putter, 2014. "A note on computing average state occupation times," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(62), pages 1681-1696.
    3. Ediev, Dalkhat M., 2010. "On the reproductive value and the spectrum of a population projection matrix with implications for dynamic population models," Theoretical Population Biology, Elsevier, vol. 78(2), pages 67-70.

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    More about this item

    Keywords

    dynamic models; population momentum; dynamic population models; eigenvalues; Leslie matrices;
    All these keywords.

    JEL classification:

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

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