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Social Security, Optimality, and Equilibria in a Stochastic Overlapping Generations Economy

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  • Gabrielle Demange
  • Guy Laroque

Abstract

Social security institutions implement intergenerational transfers and distribute risks over time. To compare various social security designs, we study an overlapping generations model with demographic shocks. Production takes place through a neoclassical production function subject to productivity shocks. We give a near characterization of optimal allocations. We study rational expectations equilibria when contributions are mandatory, based on labor and capital income. We also describe the equilibria of an economy with a voluntary pay‐as‐you‐go social security fund, and show that they have a long‐run optimality property. An example with Cobb–Douglas production and utility functions illustrates the results.

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  • Gabrielle Demange & Guy Laroque, 2000. "Social Security, Optimality, and Equilibria in a Stochastic Overlapping Generations Economy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 2(1), pages 1-23, January.
    • Handle: RePEc:bla:jpbect:v:2:y:2000:i:1:p:1-23
    DOI: 10.1111/1097-3923.00027
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    Cited by:

    1. Martin Barbie & Marten Hillebrand, 2018. "Bubbly Markov equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 627-679, October.
    2. Gottardi, Piero & Kubler, Felix, 2011. "Social security and risk sharing," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1078-1106, May.
    3. Wagener, Andreas, 2004. "On intergenerational risk sharing within social security schemes," European Journal of Political Economy, Elsevier, vol. 20(1), pages 181-206, March.
    4. Bloise, Gaetano & Reichlin, Pietro, 2011. "Asset prices, debt constraints and inefficiency," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1520-1546, July.
    5. Antoine d'Autume, 2003. "L'impact du vieillissement démographique sur les mécanismes macroéconomiques," Post-Print halshs-00452552, HAL.
    6. Antoine d'Autume, 2003. "L'impact du vieillissement démographique sur les mécanismes macroéconomiques," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00452552, HAL.
    7. Martin F. Hellwig, 2024. "Dynamic efficiency and inefficiency in a class of overlapping-generations economies with multiple assets," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2024_08, Max Planck Institute for Research on Collective Goods.
    8. Chattopadhyay, Subir, 2001. "The unit root property and optimality: a simple proof," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 151-159, November.
    9. Eisei Ohtaki & Hiroyuki Ozaki, 2014. "Optimality in a Stochastic OLG Model with Ambiguity," Working Papers e069, Tokyo Center for Economic Research.
    10. Kevin Reffett & Olivier Morand, 2008. "Isotone recursive methods for Stationary Markov Equilibra in OLG models with stochastic nonclassical production," 2008 Meeting Papers 470, Society for Economic Dynamics.
    11. Barbie, Martin & Hagedorn, Marcus & Kaul, Ashok, 2000. "Dynamic Efficiency and Pareto Optimality in a Stochastic OLG Model with Production and Social Security," IZA Discussion Papers 209, Institute of Labor Economics (IZA).
    12. Gabrielle Demange, 2009. "On Sustainable Pay‐as‐You‐Go Contribution Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(4), pages 493-527, August.
    13. Ohtaki, Eisei, 2014. "Tractable graphical device for analyzing stationary stochastic OLG economies," Journal of Macroeconomics, Elsevier, vol. 40(C), pages 16-26.
    14. Hillebrand, Marten, 2012. "On the optimal size of Social Security in the presence of a stock market," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 26-38.
    15. Roland Eisen, 2021. "Vulnerability and mutual insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 46(2), pages 224-235, April.
    16. Ohtaki, Eisei, 2013. "Golden rule optimality in stochastic OLG economies," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 60-66.
    17. Hillebrand, Marten, 2011. "On the role of labor supply for the optimal size of Social Security," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 1091-1105, July.
    18. Eisei Ohtaki, 2023. "Optimality in an OLG model with nonsmooth preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 611-659, September.
    19. Barbie, Martin & Hagedorn, Marcus & Kaul, Ashok, 2007. "On the interaction between risk sharing and capital accumulation in a stochastic OLG model with production," Journal of Economic Theory, Elsevier, vol. 137(1), pages 568-579, November.
    20. Chattopadhyay, Subir, 2018. "The unit root property and optimality with a continuum of states—Pure exchange," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 105-118.
    21. Gabay, Daniel & Grasselli, Martino, 2012. "Fair demographic risk sharing in defined contribution pension systems," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 657-669.

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