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Minimizing the dependency ratio in a population with below-replacement fertility through immigration

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  • Simon, C.
  • Belyakov, A.O.
  • Feichtinger, G.

Abstract

Many industrialized countries face fertility rates below replacement level, combined with declining mortality especially in older ages. Consequently, the populations of these countries have started to age. One important indicator of age structures is the dependency ratio which is the ratio of the nonworking age population to the working age population. In this work we find the age-specific immigration profile that minimizes the dependency ratio in a stationary population with below-replacement fertility. It is assumed that the number of immigrants per age is limited. We consider two alternative policies. In the first one, we fix the total number of people who annually immigrate to a country. In the second one, we prescribe the size of the receiving country’s population. For both cases we provide numerical results for the optimal immigration profile, for the resulting age structure of the population, as well as for the dependency ratio.

Suggested Citation

  • Simon, C. & Belyakov, A.O. & Feichtinger, G., 2012. "Minimizing the dependency ratio in a population with below-replacement fertility through immigration," Theoretical Population Biology, Elsevier, vol. 82(3), pages 158-169.
    • Handle: RePEc:eee:thpobi:v:82:y:2012:i:3:p:158-169
    DOI: 10.1016/j.tpb.2012.06.009
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    References listed on IDEAS

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    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, December.
    2. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, November.
    3. Carl Schmertmann, 2012. "Stationary populations with below-replacement fertility," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 26(14), pages 319-330.
    4. S. Mitra, 1990. "Immigration, below-replacement fertility, and long-term national population trends," Demography, Springer;Population Association of America (PAA), vol. 27(1), pages 121-129, February.
    5. Dorfman, Robert, 1969. "An Economic Interpretation of Optimal Control Theory," American Economic Review, American Economic Association, vol. 59(5), pages 817-831, December.
    6. Herbert Dawid & Gustav Feichtinger & Joshua R. Goldstein & Vladimir Veliov, 2009. "Keeping a learned society young," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 20(22), pages 541-558.
    7. Wrzaczek, Stefan & Kuhn, Michael & Prskawetz, Alexia & Feichtinger, Gustav, 2010. "The reproductive value in distributed optimal control models," Theoretical Population Biology, Elsevier, vol. 77(3), pages 164-170.
    8. Zheng Wu & Nan Li, 2003. "Immigration and the dependency ratio of a host population," Mathematical Population Studies, Taylor & Francis Journals, vol. 10(1), pages 21-39.
    9. Carl Schmertmann, 1992. "Immigrants’ ages and the structure of stationary populations with below-replacement fertility," Demography, Springer;Population Association of America (PAA), vol. 29(4), pages 595-612, November.
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    Cited by:

    1. Hassan B. Ghassan & Hassan R. Alhajhoj & Faruk Balli, 2022. "Bi-demographic and current account dynamics using SVAR model: evidence from Saudi Arabia," Economic Change and Restructuring, Springer, vol. 55(3), pages 1327-1363, August.
    2. Ghassan, Hassan & Alhajhoj, Hassan R. & Balli, Faruk, 2018. "Bi-Demographic Changes and Current Account using SVAR Modeling: Evidence from Saudi Arabia," MPRA Paper 93013, University Library of Munich, Germany, revised 01 Feb 2019.
    3. Joan C. Micó & David Soler & Maria T. Sanz & Antonio Caselles & Salvador Amigó, 2022. "Minimizing Dependency Ratio in Spain through Demographic Variables," Mathematics, MDPI, vol. 10(9), pages 1-15, April.
    4. Hassan Belkacem Ghassan & Hassan Rafdan Al-Hajhoj & Faruk Balli, 2019. "Bi-Demographic Changes and Current Account using SVAR Modeling: Evidence from Saudi Economy," Working Papers hal-01742574, HAL.
    5. Hassan B. Ghassan & Hassan R. Al-Hajhoj & Faruk Balli, 2018. "Bi-Demographic Changes and Current Account using SVAR Modeling," Papers 1803.11161, arXiv.org, revised Mar 2019.

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