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Learning to Perfect Manipulation: Implications for Fertility, Savings, and Old-Age Social Security

  • Lakshmi K Raut

In this paper we consider an overlapping gnerations model with endogenous fertility and two-sided altruism and show the limitations of applying commonly used open loop Nash equilibrium in characterizing equilibrium transfers from parents to children in the form of bequest, and transfers from children to parents as voluntary old-age support. Since in our model children are concerned with parents' old-age consumption, agents have incentives to save less for old age and to have more children so as to strategically induce their children to transfer more old-age support. We formulate such strategic behavior within a sequential multi-stage game and introduce a notion of learning equilibrium to characterize equilibrium manipulative behavior and then study the consequences of such strategic manipulations on private intergenerational transfers, fertility and savings decisions, and on Pareto optimality of equilibrium allocation. We show that the learning equilibrium notion of the paper simplifies computation of subgame perfect equilibrium, subgame perfect equilibrium is the long-run outcome of dynamic learning equilibrium paths (this aids in selecting, sometimes, a unique equilibrium among multiple subgame perfect equilibria), and an open-loop Nash equilibrium involves "incredible" threats from children. We provide an alternative explanation for the existence of publicly provided social security program and examine its role to correct distortions created by strategic manipulation.

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File URL: http://www.economics.hawaii.edu/research/workingpapers/88-98/WP_97-4.pdf
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Paper provided by University of Hawaii at Manoa, Department of Economics in its series Working Papers with number 199704.

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Length: 25 pages
Date of creation: 1997
Date of revision:
Handle: RePEc:hai:wpaper:199704
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  1. Raut, L. K., 1990. "Capital accumulation, income distribution and endogenous fertility in an overlapping generations general equilibrium model," Journal of Development Economics, Elsevier, vol. 34(1-2), pages 123-150, November.
  2. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66, pages 467.
  3. Becker, Gary S & Barro, Robert J, 1988. "A Reformulation of the Economic Theory of Fertility," The Quarterly Journal of Economics, MIT Press, vol. 103(1), pages 1-25, February.
  4. Lakshmi Kanta Raut, 1992. "Effect of Social Security on Fertility and Savings: An Overlapping Generations Model," Indian Economic Review, Department of Economics, Delhi School of Economics, vol. 27(1), pages 25-43, July.
  5. Diamond, P. A., 1977. "A framework for social security analysis," Journal of Public Economics, Elsevier, vol. 8(3), pages 275-298, December.
  6. Pollak, Robert A, 1988. "Tied Transfers and Paternalistic Preferences," American Economic Review, American Economic Association, vol. 78(2), pages 240-44, May.
  7. Bernheim, B Douglas & Shleifer, Andrei & Summers, Lawrence H, 1985. "The Strategic Bequest Motive," Journal of Political Economy, University of Chicago Press, vol. 93(6), pages 1045-76, December.
  8. P. A. Diamond & J. A. Mirrlees, 1977. "A Model of Social Insurance With Variable Retirement," Working papers 210, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Gary S. Becker, 1974. "A Theory of Social Interactions," NBER Working Papers 0042, National Bureau of Economic Research, Inc.
  10. Browning, Edgar K, 1975. "Why the Social Insurance Budget Is Too Large in a Democracy," Economic Inquiry, Western Economic Association International, vol. 13(3), pages 373-88, September.
  11. Barro, Robert J., 1974. "Are Government Bonds Net Wealth?," Scholarly Articles 3451399, Harvard University Department of Economics.
  12. Nishimura, K. & Zhang, J., 1990. "Pay-As-You-Go Public Pensions With Endogenous Fertility," Papers 202, Australian National University - Department of Economics.
  13. Kohlberg, Elon, 1976. "A model of economic growth with altruism between generations," Journal of Economic Theory, Elsevier, vol. 13(1), pages 1-13, August.
  14. Hansson, Ingemar & Stuart, Charles, 1989. "Social Security as Trade among Living Generations," American Economic Review, American Economic Association, vol. 79(5), pages 1182-95, December.
  15. Veall, Michael R., 1986. "Public pensions as optimal social contracts," Journal of Public Economics, Elsevier, vol. 31(2), pages 237-251, November.
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