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Discounting And Consumption Over An Uncertain Horizon: Draw-Down Plans For Family Trusts

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  • Stephen Satchell
  • Susan Thorp

Abstract

Individuals, endowments and trusts face uncertain lifetimes. When the planning horizon of an entity is stochastic and Pareto distributed, hyperbolic discounting and time-varying consumption rates are optimal. We derive expressions for the optimal rate of consumption (draw-down) from wealth for family trusts facing positive probabilities of extinction at each generation. Using birth statistics for the UK, we compute family extinction probabilities and show that they are well-approximated by a Pareto distribution, hence family trusts will discount hyperbolically. Numerically optimised consumption paths for family trusts with CRRA preferences are decreasing but always higher than for infinitely-lived trusts.

Suggested Citation

  • Stephen Satchell & Susan Thorp, 2008. "Discounting And Consumption Over An Uncertain Horizon: Draw-Down Plans For Family Trusts," CAMA Working Papers 2008-02, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  • Handle: RePEc:een:camaaa:2008-02
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    File URL: https://cama.crawford.anu.edu.au/sites/default/files/publication/cama_crawford_anu_edu_au/2017-02/2_satchell_thorp_2008.pdf
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    References listed on IDEAS

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    1. David I. Laibson & Andrea Repetto & Jeremy Tobacman, 1998. "Self-Control and Saving for Retirement," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 29(1), pages 91-196.
    2. Partha Dasgupta & Eric Maskin, 2005. "Uncertainty and Hyperbolic Discounting," American Economic Review, American Economic Association, vol. 95(4), pages 1290-1299, September.
    3. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-957, July.
    4. George Loewenstein & Richard H Thaler, 2003. "Anomalies: Intertemporal Choice," Levine's Working Paper Archive 618897000000000784, David K. Levine.
    5. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 185-199.
    6. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-247, April.
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    More about this item

    JEL classification:

    • G0 - Financial Economics - - General
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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