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Social security in an analytically tractable overlapping generations model with aggregate and idiosyncratic risk

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  • Harenberg, Daniel
  • Ludwig, Alexander

Abstract

When markets are incomplete, social security can partially insure against idiosyncratic and aggregate risks. We incorporate both risks into an analytically tractable model with two overlapping generations. We derive the equilibrium dynamics in closed form and show that joint presence of both risks leads to over-proportional risk exposure for households. This implies that the whole benefit from insurance through social security is greater than the sum of the benefits from insurance against each of the two risks in isolation. We measure this through interaction effects which appear even though the two risks are orthogonal by construction. While the interactions unambiguously increase the welfare benefits from insurance, they can in- or decrease the welfare costs from crowding out of capital formation. The net effect depends on the relative strengths of the opposing forces.

Suggested Citation

  • Harenberg, Daniel & Ludwig, Alexander, 2015. "Social security in an analytically tractable overlapping generations model with aggregate and idiosyncratic risk," SAFE Working Paper Series 71, Leibniz Institute for Financial Research SAFE, revised 2015.
    • Handle: RePEc:zbw:safewp:71
    DOI: 10.2139/ssrn.2515696
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    1. Alexander Ludwig & Edgar Vogel, 2010. "Mortality, fertility, education and capital accumulation in a simple OLG economy," Journal of Population Economics, Springer;European Society for Population Economics, vol. 23(2), pages 703-735, March.
    2. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-240, April.
    3. tom krebs, 2004. "welfare cost of business cycles when markets are incomplete," Econometric Society 2004 North American Summer Meetings 283, Econometric Society.
    4. Kjetil Storesletten & Chris Telmer & Amir Yaron, 2007. "Asset Pricing with Idiosyncratic Risk and Overlapping Generations," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(4), pages 519-548, October.
    5. Daniel Harenberg & Alexander Ludwig, 2019. "Idiosyncratic Risk, Aggregate Risk, And The Welfare Effects Of Social Security," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(2), pages 661-692, May.
    6. Matsen, Egil & Thogersen, Oystein, 2004. "Designing social security - a portfolio choice approach," European Economic Review, Elsevier, vol. 48(4), pages 883-904, August.
    7. Cass, David, 1972. "On capital overaccumulation in the aggregative, neoclassical model of economic growth: A complete characterization," Journal of Economic Theory, Elsevier, vol. 4(2), pages 200-223, April.
    8. Alexander Ludwig & Michael Reiter, 2010. "Sharing Demographic Risk--Who Is Afraid of the Baby Bust?," American Economic Journal: Economic Policy, American Economic Association, vol. 2(4), pages 83-118, November.
    9. Daniel Harenberg & Alexander Ludwig, "undated". "Social Security and the Interactions Between Aggregate and Idiosyncratic Risk," Working Papers ETH-RC-14-002, ETH Zurich, Chair of Systems Design.
    10. Tom Krebs, 2007. "Job Displacement Risk and the Cost of Business Cycles," American Economic Review, American Economic Association, vol. 97(3), pages 664-686, June.
    11. Henning Bohn, 2001. "Social Security and Demographic Uncertainty: The Risk-Sharing Properties of Alternative Policies," NBER Chapters, in: Risk Aspects of Investment-Based Social Security Reform, pages 203-246, National Bureau of Economic Research, Inc.
    12. Laurence Ball & N. Gregory Mankiw, 2007. "Intergenerational Risk Sharing in the Spirit of Arrow, Debreu, and Rawls, with Applications to Social Security Design," Journal of Political Economy, University of Chicago Press, vol. 115(4), pages 523-547, August.
    13. Franke, Guenter & Schlesinger, Harris & Stapleton, Richard C., 2011. "Risk taking with additive and multiplicative background risks," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1547-1568, July.
    14. Frank Caliendo & Nick Guo & Roozbeh Hosseini, 2014. "Social Security is NOT a Substitute for Annuity Markets," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 739-755, October.
    15. Huffman, Gregory W, 1987. "A Dynamic Equilibrium Model of Asset Prices and Transaction Volume," Journal of Political Economy, University of Chicago Press, vol. 95(1), pages 138-159, February.
    16. Dirk Krueger & Felix Kubler, 2006. "Pareto-Improving Social Security Reform when Financial Markets are Incomplete!?," American Economic Review, American Economic Association, vol. 96(3), pages 737-755, June.
    17. Fatih Guvenen & Serdar Ozkan & Jae Song, 2014. "The Nature of Countercyclical Income Risk," Journal of Political Economy, University of Chicago Press, vol. 122(3), pages 621-660.
    18. Auerbach, Alan J. & Hassett, Kevin, 2007. "Optimal long-run fiscal policy: Constraints, preferences and the resolution of uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1451-1472, May.
    19. Imrohoroglu, Ayse & Imrohoroglu, Selahattin & Joines, Douglas H, 1998. "The Effect of Tax-Favored Retirement Accounts on Capital Accumulation," American Economic Review, American Economic Association, vol. 88(4), pages 749-768, September.
    20. Bohn, Henning, 2009. "Intergenerational risk sharing and fiscal policy," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 805-816, September.
    21. Olovsson, Conny, 2010. "Quantifying the risk-sharing welfare gains of social security," Journal of Monetary Economics, Elsevier, vol. 57(3), pages 364-375, April.
    22. Diamond, P. A., 1977. "A framework for social security analysis," Journal of Public Economics, Elsevier, vol. 8(3), pages 275-298, December.
    23. Jasmina Hasanhodzic & Laurence J. Kotlikoff, 2013. "Generational Risk–Is It a Big Deal?: Simulating an 80-Period OLG Model with Aggregate Shocks," BYU Macroeconomics and Computational Laboratory Working Paper Series 2013-01, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    24. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    25. Mankiw, N. Gregory, 1986. "The equity premium and the concentration of aggregate shocks," Journal of Financial Economics, Elsevier, vol. 17(1), pages 211-219, September.
    26. Gordon, Roger H. & Varian, Hal R., 1988. "Intergenerational risk sharing," Journal of Public Economics, Elsevier, vol. 37(2), pages 185-202, November.
    27. Roozbeh Hosseini & Lei (Nick) Guo & Frank Caliendo, 2013. "Social Security is NOT a Substitute for Annuities," 2013 Meeting Papers 680, Society for Economic Dynamics.
    28. Massimiliano De Santis, 2007. "Individual Consumption Risk and the Welfare Cost of Business Cycles," American Economic Review, American Economic Association, vol. 97(4), pages 1488-1506, September.
    29. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    30. Kjetil Storesletten & Chris I. Telmer & Amir Yaron, 2004. "Cyclical Dynamics in Idiosyncratic Labor Market Risk," Journal of Political Economy, University of Chicago Press, vol. 112(3), pages 695-717, June.
    31. Imrohoroglu, Ayse & Imrohoroglu, Selahattin & Joines, Douglas H, 1995. "A Life Cycle Analysis of Social Security," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(1), pages 83-114, June.
    32. Juan C. Conesa & Dirk Krueger, 1999. "Social Security Reform with Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 2(4), pages 757-795, October.
    33. repec:mea:meawpa:14280 is not listed on IDEAS
    34. Robert C. Merton, 1983. "On the Role of Social Security as a Means for Efficient Risk Sharing in an Economy Where Human Capital Is Not Tradable," NBER Chapters, in: Financial Aspects of the United States Pension System, pages 325-358, National Bureau of Economic Research, Inc.
    35. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Oliwia Komada & Krzysztof Makarski & Joanna Tyrowicz, 2017. "Welfare effects of fiscal policy in reforming the pension system," GRAPE Working Papers 11, GRAPE Group for Research in Applied Economics.
    2. Daniel Harenberg & Alexander Ludwig, "undated". "Social Security and the Interactions Between Aggregate and Idiosyncratic Risk," Working Papers ETH-RC-14-002, ETH Zurich, Chair of Systems Design.
    3. Krueger, Dirk & Ludwig, Alexander & Villalvazo, Sergio, 2021. "Optimal taxes on capital in the OLG model with uninsurable idiosyncratic income risk," Journal of Public Economics, Elsevier, vol. 201(C).
    4. Jaimes, Richard & Westerhout, Ed, 2023. "Optimal policies in an ageing society," The Journal of the Economics of Ageing, Elsevier, vol. 26(C).
    5. Anna Batyra & David de la Croix & Olivier Pierrard & Henri Sneessens, 2016. "Structural changes in the labor market and the rise of early retirement in Europe," DEM Discussion Paper Series 16-13, Department of Economics at the University of Luxembourg.
    6. James Staveley-O'Carroll & Olena Staveley-O'Carroll, 2019. "International Welfare Spillovers of National Pension Schemes," Working Papers 1903, College of the Holy Cross, Department of Economics.
    7. Jaimes, Richard, 2023. "Does idiosyncratic risk matter for climate policy?," Environment and Development Economics, Cambridge University Press, vol. 28(4), pages 353-367, August.
    8. Daniel Harenberg & Alexander Ludwig, 2019. "Idiosyncratic Risk, Aggregate Risk, And The Welfare Effects Of Social Security," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(2), pages 661-692, May.
    9. Shantanu Bagchi, 2024. "Business Cycles and Public Pensions: Aggregate Risk and Social Security in the United States," Working Papers 2024-11, Towson University, Department of Economics, revised Sep 2024.
    10. Staveley-O’Carroll James & Staveley-O’Carroll Olena M., 2021. "International Welfare Spillovers of National Pension Schemes," The B.E. Journal of Macroeconomics, De Gruyter, vol. 21(1), pages 363-397, January.
    11. Bommier, Antoine & Harenberg, Daniel & Le Grand, François, 2017. "Household Finance and the Value of Life," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168189, Verein für Socialpolitik / German Economic Association.
    12. Makarski, Krzysztof & Tyrowicz, Joanna & Komada, Oliwia, 2021. "Efficiency versus Insurance: Capital Income Taxation and Privatizing Social Security," IZA Discussion Papers 14805, Institute of Labor Economics (IZA).

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    More about this item

    Keywords

    social security; idiosyncratic risk; aggregate risk; welfare; insurance; crowding out;
    All these keywords.

    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E27 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Forecasting and Simulation: Models and Applications
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • H55 - Public Economics - - National Government Expenditures and Related Policies - - - Social Security and Public Pensions

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