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Optimal Fertility along the Lifecycle

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  • Pierre Pestieau

    (PSE - Paris-Jourdan Sciences Economiques - CNRS : UMR8545 - École des Hautes Études en Sciences Sociales (EHESS) - École des Ponts ParisTech (ENPC) - École normale supérieure [ENS] - Paris - Institut national de la recherche agronomique (INRA), EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, CREPP - Center of Research in Public Economics and Population Economics - Université de Liège, CORE - Center of Operation Research and Econometrics [Louvain] - Université Catholique de Louvain (UCL) - Belgique, CEPR - Center for Economic Policy Research - CEPR)

  • Grégory Ponthière

    (PSE - Paris-Jourdan Sciences Economiques - CNRS : UMR8545 - École des Hautes Études en Sciences Sociales (EHESS) - École des Ponts ParisTech (ENPC) - École normale supérieure [ENS] - Paris - Institut national de la recherche agronomique (INRA), EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, ENS Paris - Ecole Normale Supérieure de Paris - École normale supérieure [ENS] - Paris)

Abstract

We explore the optimal fertility age-pattern in a four-period OLG economy with physical capital accumulation. For that purpose, we .rstly compare the dynamics of two closed economies, Early and Late Islands, which di¤er only in the timing of births. On Early Island, children are born from parents in young adulthood, whereas, on Late Island, children are born from parents in older adulthood. We show that, unlike on Early Island, there exists no stable stationary equilibrium on Late Island, which exhibits cyclical dynamics. We also characterize the social optimum in each economy, and show that Samuelson.s Serendipity Theorem still holds. Finally, we study the dynamics and social optimum of an economy with interior fertility rates during the reproduction period. It is shown that various fertility age-patterns are compatible with the social optimum, as long as these yield the optimal cohort growth rate. The Serendipity Theorem remains valid in that broader demographic environment.

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Bibliographic Info

Paper provided by HAL in its series PSE Working Papers with number hal-00612609.

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Date of creation: Jul 2011
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Handle: RePEc:hal:psewpa:hal-00612609

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Keywords: childbearing ages ; early and late motherhoods ; fertility ; overlapping generations ; social optimum;

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  1. Samuelson, Paul A, 1975. "The Optimum Growth Rate for Population," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(3), pages 531-38, October.
  2. David Croix & Pierre Pestieau & Grégory Ponthière, 2012. "How powerful is demography? The Serendipity Theorem revisited," Journal of Population Economics, Springer, vol. 25(3), pages 899-922, July.
  3. Klaus Jaeger & Wolfgang Kuhle, 2009. "The optimum growth rate for population reconsidered," Journal of Population Economics, Springer, vol. 22(1), pages 23-41, January.
  4. G. ABIO & Géraldine MAHIEU & C. Patxot, 2002. "On the Optimality of PAYG Pension Systems in an Endogenous Fertility Setting," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2002006, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  5. Ermisch, John & Ogawa, Naohiro, 1994. "Age at Motherhood in Japan," Journal of Population Economics, Springer, vol. 7(4), pages 393-420, November.
  6. Siv Gustafsson, 2001. "Optimal age at motherhood. Theoretical and empirical considerations on postponement of maternity in Europe," Journal of Population Economics, Springer, vol. 14(2), pages 225-247.
  7. Mordecai Kurz, 2011. "Symposium: on the role of market belief in economic dynamics, an introduction," Economic Theory, Springer, vol. 47(2), pages 189-204, June.
  8. John Ermisch & David Pevalin, 2005. "Early motherhood and later partnerships," Journal of Population Economics, Springer, vol. 18(3), pages 469-489, 09.
  9. David De La Croix & Géraldine Mahieu & Alexandra Rillaers, 2004. "How Should the Allocation of Resources Adjust to the Baby Bust?," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(4), pages 607-636, October.
  10. Gemma Abio Roig, 2003. "Interiority of the Optimal Population Growth Rate with Endogenous Fertility," Working Papers in Economics 96, Universitat de Barcelona. Espai de Recerca en Economia.
  11. MICHEL, Philippe & PESTIEAU, Pierre, . "Population growth and optimality. When does serendipity hold?," CORE Discussion Papers RP -1072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. de la Croix,David & Michel,Philippe, 2002. "A Theory of Economic Growth," Cambridge Books, Cambridge University Press, number 9780521806428, October.
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  14. Cigno, Alessandro & Ermisch, John, 1989. "A microeconomic analysis of the timing of births," European Economic Review, Elsevier, vol. 33(4), pages 737-760, April.
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  16. DE LA CROIX, David & MAHIEU, Géraldine & RILLAERS, Alexandra, . "How should the allocation of resources adjust to the baby bust?," CORE Discussion Papers RP -1741, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521551861, October.
  18. Blackburn, Keith & Cipriani, Giam Pietro, 2002. "A model of longevity, fertility and growth," Journal of Economic Dynamics and Control, Elsevier, vol. 26(2), pages 187-204, February.
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  20. Pierre Pestieau & Grégory Ponthière, 2012. "Optimal Lifecycle Fertility in a Barro Becker Economy," PSE Working Papers halshs-00676500, HAL.
  21. Deardorff, Alan V, 1976. "The Optimum Growth Rate for Population: Comment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 510-15, June.
  22. Heather Joshi, 2002. "Production, Reproduction, and Education: Women, Children, and Work in a British Perspective," Population and Development Review, The Population Council, Inc., vol. 28(3), pages 445-474.
  23. Aditya Goenka & Lin Liu, 2012. "Infectious diseases and endogenous fluctuations," Economic Theory, Springer, vol. 50(1), pages 125-149, May.
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  25. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Schubert, Katheline, 2010. "Demographic-economic equilibria when the age at motherhood is endogenous," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1211-1221, November.
  26. Ehrlich, Isaac & Lui, Francis T, 1991. "Intergenerational Trade, Longevity, and Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 1029-59, October.
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Citations

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Cited by:
  1. Pierre Pestieau & Grégory Ponthière, 2011. "Childbearing Age, Family Allowances and Social Security," PSE Working Papers hal-00612613, HAL.
  2. repec:hal:wpaper:halshs-00676500 is not listed on IDEAS
  3. Pierre Pestieau & Grégory Ponthière, 2012. "Optimal Lifecycle Fertility in a Barro Becker Economy," PSE Working Papers halshs-00676500, HAL.
  4. repec:hal:wpaper:hal-00612613 is not listed on IDEAS
  5. Thomas Renstrom & Luca Spataro, 2014. "Population growth and human capital: a welfarist approach," Public Finance Research Papers 3, Istituto di Economia e Finanza, DIGEF, Sapienza University of Rome.

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