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Fertility-related pensions and cyclical instability

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  • Luciano Fanti
  • Luca Gori

Abstract

In this paper, we study a general equilibrium model with overlapping generations, endogenous fertility and public pensions. By assuming Cobb–Douglas technology and logarithmic preferences, we show that the introduction of a fertility-related component in the pay-as-you-go pension scheme may destabilise the long-term equilibrium and cause endogenous fluctuations when individuals have static expectations. The possibility of cyclical instability increases (resp. reduces) when both the subjective discount factor and relative weight of individual fertility in pay-as-you-go pensions (resp. the parents’ taste for children) increase(s). Interestingly, when public pensions are contingent on the individual number of children, the financing of small-sized benefits may cause the occurrence of a flip bifurcation, two-period cycles and cycles of a higher order. In addition, we show through numerical simulations that these results hold in a more general setting with a constant inter-temporal elasticity of substitution utility function and a constant elasticity of substitution production function. Our findings identify a possible novel factor responsible for persistent deterministic fluctuations in a context of overlapping generations, while also representing a policy warning regarding the destabilising effects of fertility-related pension reforms, which are currently high in both the theoretical debate and the political agendas of several developed countries. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Luciano Fanti & Luca Gori, 2013. "Fertility-related pensions and cyclical instability," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(3), pages 1209-1232, July.
  • Handle: RePEc:spr:jopoec:v:26:y:2013:i:3:p:1209-1232
    DOI: 10.1007/s00148-012-0462-4
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    1. Author-Name: Alan S. Blinder & Alan B. Krueger, 2004. "What Does the Public Know about Economic Policy, and How Does It Know It?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 35(1), pages 327-397.
    2. Hommes, Cars H., 1991. "Adaptive learning and roads to chaos : The case of the cobweb," Economics Letters, Elsevier, vol. 36(2), pages 127-132, June.
    3. Zhang, Jie & Zhang, Junsen & Lee, Ronald, 2003. "Rising longevity, education, savings, and growth," Journal of Development Economics, Elsevier, vol. 70(1), pages 83-101, February.
    4. Cigno, Alessandro, 1995. "Public pensions with endogenous fertility: Comment on Nishimura and Zhang," Journal of Public Economics, Elsevier, vol. 57(1), pages 169-173, May.
    5. de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
    6. Gary S. Becker & H. Gregg Lewis, 1974. "Interaction between Quantity and Quality of Children," NBER Chapters, in: Economics of the Family: Marriage, Children, and Human Capital, pages 81-90, National Bureau of Economic Research, Inc.
    7. Alessandro Cigno, 2010. "How to Avoid a Pension Crisis: A Question of Intelligent System Design ," CESifo Economic Studies, CESifo, vol. 56(1), pages 21-37, March.
    8. Antoci, Angelo & Sodini, Mauro, 2009. "Indeterminacy, bifurcations and chaos in an overlapping generations model with negative environmental externalities," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1439-1450.
    9. Barkley Rosser, J. Jr., 2001. "Complex ecologic-economic dynamics and environmental policy," Ecological Economics, Elsevier, vol. 37(1), pages 23-37, April.
    10. Martin Kolmar, 1997. "Intergenerational redistribution in a small open economy with endogenous fertility," Journal of Population Economics, Springer;European Society for Population Economics, vol. 10(3), pages 335-356.
    11. Bas Groezen & Lex Meijdam, 2008. "Growing old and staying young: population policy in an ageing closed economy," Journal of Population Economics, Springer;European Society for Population Economics, vol. 21(3), pages 573-588, July.
    12. Junxi Zhang, 1999. "Environmental sustainability, nonlinear dynamics and chaos," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 489-500.
    13. Robert Fenge & Volker Meier, 2005. "Pensions and fertility incentives," Canadian Journal of Economics, Canadian Economics Association, vol. 38(1), pages 28-48, February.
    14. Rowena A. Pecchenino & Patricia S. Pollard, 2005. "Aging, Myopia, and the Pay‐As‐You‐Go Public Pension Systems of the G7: A Bright Future?," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(3), pages 449-470, August.
    15. Bental, Benjamin, 1989. "The Old Age Security Hypothesis and Optimal Population Growth," Journal of Population Economics, Springer;European Society for Population Economics, vol. 1(4), pages 285-301.
    16. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    17. Michel, Philippe & de la Croix, David, 2000. "Myopic and perfect foresight in the OLG model," Economics Letters, Elsevier, vol. 67(1), pages 53-60, April.
    18. Lund, Jesper & Engsted, Tom, 1996. "GMM and present value tests of the C-CAPM: evidence from the Danish, German, Swedish and UK stock markets," Journal of International Money and Finance, Elsevier, vol. 15(4), pages 497-521, August.
    19. Eckstein, Zvi & Stern, Steven & Wolpin, Kenneth I, 1988. "Fertility Choice, Land, and the Malthusian Hypothesis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(2), pages 353-361, May.
    20. Douglas Gollin, 2002. "Getting Income Shares Right," Journal of Political Economy, University of Chicago Press, vol. 110(2), pages 458-474, April.
    21. Robert Fenge & Jakob Weizsäcker, 2010. "Mixing Bismarck and child pension systems: an optimum taxation approach," Journal of Population Economics, Springer;European Society for Population Economics, vol. 23(2), pages 805-823, March.
    22. Luciano Fanti & Luca Spataro, 2008. "Poverty traps and intergenerational transfers," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 15(6), pages 693-711, December.
    23. Hall, Robert E, 1988. "Intertemporal Substitution in Consumption," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 339-357, April.
    24. Alessandro Cigno & Luca Casolaro & Furio C. Rosati, 2002. "The Impact of Social Security on Saving and Fertility in Germany," FinanzArchiv: Public Finance Analysis, Mohr Siebeck, Tübingen, vol. 59(2), pages 189-211, May.
    25. Zhang, Junsen & Zhang, Jie & Lee, Ronald, 2001. "Mortality decline and long-run economic growth," Journal of Public Economics, Elsevier, vol. 80(3), pages 485-507, June.
    26. Chen, Hung-Ju & Li, Ming-Chia & Lin, Yung-Ju, 2008. "Chaotic dynamics in an overlapping generations model with myopic and adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 48-56, July.
    27. Junsen Zhang & Junxi Zhang, 1998. "Social Security, Intergenerational Transfers, and Endogenous Growth," Canadian Journal of Economics, Canadian Economics Association, vol. 31(5), pages 1225-1241, November.
    28. Farmer, Roger E. A., 1986. "Deficits and cycles," Journal of Economic Theory, Elsevier, vol. 40(1), pages 77-88, October.
    29. Samuelson, Paul A, 1975. "Optimum Social Security in a Life-Cycle Growth Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(3), pages 539-544, October.
    30. Luca Spataro & Luciano Fanti, 2011. "The Optimal Level of Debt in an OLG Model with Endogenous Fertility," German Economic Review, Verein für Socialpolitik, vol. 12(3), pages 351-369, August.
    31. Masao Ogaki & Carmen M. Reinhart, 1998. "Measuring Intertemporal Substitution: The Role of Durable Goods," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 1078-1098, October.
    32. Eric Girardin & Lucio Sarno & Mark P. Taylor, 2000. "Private consumption behaviour, liquidity constraints and financial deregulation in France: a nonlinear analysis," Empirical Economics, Springer, vol. 25(2), pages 351-368.
    33. Robert Fenge & Volker Meier, 2009. "Are family allowances and fertility-related pensions perfect substitutes?," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 16(2), pages 137-163, April.
    34. Jess Benhabib & Kazuo Nishimura, 2012. "The Hopf Bifurcation and Existence and Stability of Closed Orbits in Multisector Models of Optimal Economic Growth," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 51-73, Springer.
    35. Eckstein, Zvi & Wolpin, Kenneth I., 1985. "Endogenous fertility and optimal population size," Journal of Public Economics, Elsevier, vol. 27(1), pages 93-106, June.
    36. Luciano Fanti & Luca Gori, 2012. "Fertility and PAYG pensions in the overlapping generations model," Journal of Population Economics, Springer;European Society for Population Economics, vol. 25(3), pages 955-961, July.
    37. de la Croix,David & Michel,Philippe, 2002. "A Theory of Economic Growth," Cambridge Books, Cambridge University Press, number 9780521001151, April.
    38. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
    39. Stuart Hyde & Keith Cuthbertson & Dirk Nitzsche, 2005. "Resuscitating the C-CAPM: empirical evidence from France and Germany," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 10(4), pages 337-357.
    40. Martin Feldstein, 2005. "Structural Reform of Social Security," Journal of Economic Perspectives, American Economic Association, vol. 19(2), pages 33-55, Spring.
    41. Michele Boldrin & Larry E. Jones, 2002. "Mortality, Fertility, and Saving in a Malthusian Economy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 5(4), pages 775-814, October.
    42. Alessandro Cigno & Annalisa Luporini & Anna Pettini, 2004. "Hidden information problems in the design of family allowances," Journal of Population Economics, Springer;European Society for Population Economics, vol. 17(4), pages 645-655, December.
    43. Abã O, G. & Mahieu, G. & Patxot, C., 2004. "On the optimality of PAYG pension systems in an endogenous fertility setting," Journal of Pension Economics and Finance, Cambridge University Press, vol. 3(1), pages 35-62, March.
    44. Alessandro Cigno & Martin Werding, 2007. "Children and Pensions," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033690.
    45. van Groezen, Bas & Leers, Theo & Meijdam, Lex, 2003. "Social security and endogenous fertility: pensions and child allowances as siamese twins," Journal of Public Economics, Elsevier, vol. 87(2), pages 233-251, February.
    46. Berthold U. Wigger, 1999. "Pay-as-you-go financed public pensions in a model of endogenous growth and fertility," Journal of Population Economics, Springer;European Society for Population Economics, vol. 12(4), pages 625-640.
    47. Tito Boeri & Axel Boersch-Supan & Guido Tabellini, 2002. "Pension Reforms and the Opinions of European Citizens," American Economic Review, American Economic Association, vol. 92(2), pages 396-401, May.
    48. Hommes, Cars H., 1994. "Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 315-335, August.
    49. Cigno, Alessandro, 1986. "Fertility and the Tax-Benefit System: A Reconsideration of the Theory of Family Taxation," Economic Journal, Royal Economic Society, vol. 96(384), pages 1035-1051, December.
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    Cited by:

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    3. Cigno, A., 2016. "Conflict and Cooperation Within the Family, and Between the State and the Family, in the Provision of Old-Age Security," Handbook of the Economics of Population Aging, in: Piggott, John & Woodland, Alan (ed.), Handbook of the Economics of Population Aging, edition 1, volume 1, chapter 0, pages 609-660, Elsevier.
    4. Luciano Fanti & Luca Gori, 2014. "Endogenous fertility, endogenous lifetime and economic growth: the role of child policies," Journal of Population Economics, Springer;European Society for Population Economics, vol. 27(2), pages 529-564, April.
    5. Kontogiannis, Nikolaos & Litina, Anastasia & Varvarigos, Dimitrios, 2019. "Occupation-induced status, social norms, and economic growth," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 348-360.
    6. Luciano Fanti & Luca Gori, 2014. "An OLG model of growth with longevity: when grandparents take care of grandchildren," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 13(1), pages 39-51, April.
    7. Luciano Fanti & Luca Gori & Cristiana Mammana & Elisabetta Michetti, 2018. "A model of growth with inherited tastes," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 163-186, November.
    8. Luciano, Fanti & Luca, Gori & Cristiana, Mammana & Elisabetta, Michetti, 2016. "Complex dynamics in an OLG model of growth with inherited tastes," MPRA Paper 69906, University Library of Munich, Germany.
    9. Gurgen Aslanyan, 2014. "The migration challenge for PAYG," Journal of Population Economics, Springer;European Society for Population Economics, vol. 27(4), pages 1023-1038, October.
    10. Dimitrios Varvarigos, 2017. "Endogenous cycles and human capital," Journal of Economics, Springer, vol. 120(1), pages 31-45, January.
    11. Masaya Yasuoka, 2018. "Fertility and education investment incentive with a pay-as-you-go pension," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 8(1), pages 37-50, April.
    12. Cipriani, Giam Pietro & Fioroni, Tamara, 2021. "Social Security and Endogenous Demographic Change: Child Support and Retirement Policies," IZA Discussion Papers 14018, Institute of Labor Economics (IZA).
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    More about this item

    Keywords

    Endogenous fertility; Fertility-related pensions; Static expectations; OLG model; C62; H55; J14; J18; J26;
    All these keywords.

    JEL classification:

    • H55 - Public Economics - - National Government Expenditures and Related Policies - - - Social Security and Public Pensions
    • J14 - Labor and Demographic Economics - - Demographic Economics - - - Economics of the Elderly; Economics of the Handicapped; Non-Labor Market Discrimination
    • J18 - Labor and Demographic Economics - - Demographic Economics - - - Public Policy
    • J26 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Retirement; Retirement Policies
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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