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Two-Sex Demographic Models

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  • Pollak, Robert A

Abstract

Classical stable population theory, the standard model of population age structure and growth, is ill suited to addressing many issues that concern economists and demographers because it is a "one-sex" theory. This paper investigates the existence, uniqueness, and dynamic stability of equilibrium in the birth matrix-mating rule model, a new model of age structure and growth for two-sex, monogamously mating, populations. The paper shows, by means of examples, that the birth matrix-mating rule model can have multiple nontrivial equilibria and establishes sufficient conditions for uniqueness. It generalizes a theorem of W. Brian Arthur to nonlinear systems and uses it to establish sufficient conditions for local dynamic stability. Copyright 1990 by University of Chicago Press.

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  • Pollak, Robert A, 1990. "Two-Sex Demographic Models," Journal of Political Economy, University of Chicago Press, vol. 98(2), pages 399-420, April.
    • Handle: RePEc:ucp:jpolec:v:98:y:1990:i:2:p:399-420
    DOI: 10.1086/261683
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    Cited by:

    1. Alpern, Steve & Katrantzi, Ioanna & Ramsey, David, 2014. "Equilibrium population dynamics when mating is by mutual choice based on age," Theoretical Population Biology, Elsevier, vol. 94(C), pages 63-72.
    2. John Dagsvik & Helge Brunborg & Ane Flaatten, 2001. "A behavioral two-sex marriage model," Mathematical Population Studies, Taylor & Francis Journals, vol. 9(2), pages 97-121.
    3. Edoardo Ciscato, 2019. "Matching models with and without frictions : applications to the economics of the family [Modèles d'appariement avec et sans frictions : applications à l'économie de la famille]," SciencePo Working papers tel-03411916, HAL.
    4. Sudeshna Maitra, 2006. "Population Growth and Rising Dowries: The Long-Run Mechanism of a Marriage Squeeze," Working Papers 2006_9, York University, Department of Economics.
    5. de Vries, Charlotte & Caswell, Hal, 2019. "Selection in two-sex stage-structured populations: Genetics, demography, and polymorphism," Theoretical Population Biology, Elsevier, vol. 130(C), pages 160-169.
    6. Aloysius Siow & Eugene Choo, 2007. "Lifecycle marriage matching: Theory and Evidence," 2007 Meeting Papers 550, Society for Economic Dynamics.
    7. Rune Johansen & John K. Dagsvik, 1999. "The Dynamics of a Behavioral Two-Sex Demographic Model," Discussion Papers 247, Statistics Norway, Research Department.
    8. Eugene Choo & Aloysius Siow, 2006. "Estimating a marriage matching model with spillover effects," Demography, Springer;Population Association of America (PAA), vol. 43(3), pages 463-490, August.
    9. Alexander Sinelnikov, 2017. "Demographics in the “Marriage Market†of the Sverdlovsk Region," Economy of region, Centre for Economic Security, Institute of Economics of Ural Branch of Russian Academy of Sciences, vol. 1(4), pages 1164-1174.
    10. Aloysius Siow & Xiaodong Zhu, 2002. "Differential Fecundity and Gender-Biased Parental Investments in Health," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 5(4), pages 999-1024, October.
    11. Edoardo Ciscato, 2019. "Matching models with and without frictions : applications to the economics of the family [Modèles d'appariement avec et sans frictions : applications à l'économie de la famille]," SciencePo Working papers Main tel-03411916, HAL.
    12. Robert A. Pollak, 2004. "An intergenerational model of domestic violence," Journal of Population Economics, Springer;European Society for Population Economics, vol. 17(2), pages 311-329, June.
    13. Noël Bonneuil & Elena Fursa, 2012. "Optimal Marriage Fitting for Imperfect Statistics," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 532-545, May.
    14. Lee, Ronald D., 2019. "Samuelson's Contributions to Population Theory and Overlapping Generations in Economics," IZA Discussion Papers 12442, Institute of Labor Economics (IZA).
    15. Xi Song & Robert D. Mare, 2017. "Short-Term and Long-Term Educational Mobility of Families: A Two-Sex Approach," Demography, Springer;Population Association of America (PAA), vol. 54(1), pages 145-173, February.

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