Journal of Population Economics

, Volume 30, Issue 2, pp 621–646 | Cite as

Optimal fertility under age-dependent labour productivity

Original Paper

Abstract

In the so-called Rapport Sauvy (1962), the French demographer Alfred Sauvy argued that Wallonia’s fertility rate was socially suboptimal, and recommended a 20 % rise of fertility, on the grounds that a society with too low a fertility leads to a low-productive economy composed of old workers having old ideas. This paper examines how Sauvy’s intuition can be incorporated in the Samuelsonian optimal fertility model (Samuelson, Int Econ Rev 16:531–538, 1975). We build a four-period OLG model with physical capital and with two generations of workers (young and old), the skills of the latter being subject to some form of decay. We characterize the optimal fertility rate and show that this equalizes, at the margin, the sum of the capital dilution effect (Solow effect) and the labour age-composition effect (Sauvy effect) with the intergenerational redistribution effect (Samuelson effect). Numerical simulations show that it is hard, from a quantitative perspective, to reconcile Sauvy’s recommendation with facts. This leads us to examine other potential determinants of optimal fertility, by introducing technological progress and a more general social welfare function.

Keywords

Optimal fertility Age structure Labour productivity Overlapping generations Social optimum 

JEL Classification

E13 E21 J13 J24 

References

  1. Abio G (2003) Interiority of the optimal population growth rate with endogenous fertility. Econ Bull 10(4):1–7Google Scholar
  2. Aubert P, Crépon B (2007) Are older workers less productive? Firm-level evidence on age-productivity and age-wages profiles. mimeoGoogle Scholar
  3. Blackorby C, Bossert W, Donaldson D (2005) Population issues in social choice theory, welfare economics and ethics. Cambridge University PressGoogle Scholar
  4. Blundell R, Browning M, Meghir C (1994) Consumer demand and the life-cycle allocation of household expenditures. Rev Econ Stud 61(1):57–80CrossRefGoogle Scholar
  5. Börsch-Supan A, Weiss M (2016) Productivity and age: evidence from work teams at the assembly line. The Journal of the Economics of Ageing 7:30–42CrossRefGoogle Scholar
  6. Boucekkine R, de la Croix D, Licandro O (2002) Vintage human capital, demographic trends and endogenous growth. J Econ Theory 104(2):340–375CrossRefGoogle Scholar
  7. Browning M, Hansen L, Heckman J (1999) Micro data and general equilibrium models. In: Taylor J, Woodford M (eds) Handbook of macroeconomics, vol 1A. Elsevier ScienceGoogle Scholar
  8. Capron C, Debuissson M, Eggerickx T, Poulain M (1998) La Dualité démographique de la Belgique: mythe ou réalité?. In: Régimes démographiques et territoires: les frontières en question : colloque international de la rochelle, 22–26 Septembre 1998Google Scholar
  9. Deardorff AV (1976) The optimum growth rate for population: comment. Int Econ Rev 17(5):510–515CrossRefGoogle Scholar
  10. de la Croix D, Michel P (2002) A theory of economic growth. Dynamics and policy in overlapping generations. Cambridge University PressGoogle Scholar
  11. de la Croix D, Pestieau P, Ponthiere G (2012) How powerful is demography? The serendipity theorem revisited. J Popul Econ 25:899–922CrossRefGoogle Scholar
  12. Del Rey E, Lopez-Garcia M-A (2013) Optimal education and pensions in an endogenous growth model. J Econ Theory 148(4):1737–1750CrossRefGoogle Scholar
  13. Göbel C, Zwick T (2012) Age and productivity: sector differences. De Economist 160(1):35–57CrossRefGoogle Scholar
  14. Greenwood J, Seshadri A, Vandenbroucke G (2005) The baby boom and baby bust. Am Econ Rev 95(1):183–207CrossRefGoogle Scholar
  15. Johnson P (1993) Aging and European economic demography. In: Johnson P, Zimmermann K (eds) Labor markets in an ageing europe. Cambridge University press, CambridgeGoogle Scholar
  16. Jones L, Schoonbroodt A (2016) Baby busts and baby booms: the fertility response to shocks in dynastic models. MimeoGoogle Scholar
  17. Michel P, Pestieau P (1993) Population growth and optimality: when does the serendipity hold. J Popul Econ 6:353–362CrossRefGoogle Scholar
  18. Ng Y-K (1986) Social criteria for evaluating population change: an alternative to the Blackorby-Donaldson criterion. J Public Econ 29:375–381CrossRefGoogle Scholar
  19. Parfit D (1984) Reasons and persons. Oxford University PressGoogle Scholar
  20. Pestieau P, Ponthiere G (2014) Optimal fertility along the life cycle. Economic Theory 55(1):185–224CrossRefGoogle Scholar
  21. Phelps E (1961) The golden rule of accumulation: a fable for growthmen. Am Econ Rev 51(4):638–643Google Scholar
  22. Samuelson P (1975) The optimum growth rate for population. Int Econ Rev 16:531–538CrossRefGoogle Scholar
  23. Sauvy A (1956) Théorie générale de la population. Volume 1: économie et population. Presses Universitaires de FranceGoogle Scholar
  24. Sauvy A (1962) Le rapport Sauvy sur le problème de l’économie et de la population en Wallonie. Editions du Conseil Economique Wallon, LiègeGoogle Scholar
  25. Skirbekk V (2003) Age and individual productivity: a literature survey. In: Feichtinger G (ed) Vienna yearbook of population research. Austrian Academy of Sciences Press, Vienna, p 2004Google Scholar
  26. Stelter R (2016) Over-aging—are present human populations too old? Mathematical Social Sciences. forthcomingGoogle Scholar
  27. van Ours J, Stoeldraijer L (2010) Age, wage and productivity. IZA Discussion Paper:4765Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.CORE and Paris School of EconomicsUniversity of LiegeLiegeBelgium
  2. 2.Paris School of EconomicsUniversity Paris East (ERUDITE)ParisFrance
  3. 3.Institut Universitaire de FranceParisFrance

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