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

  • Stephen Satchell

    ()

  • Susan Thorp

    ()

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.

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File URL: http://cbe.anu.edu.au/research/papers/camawpapers/Papers/2008/Satchell_Thorp_22008.pdf
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Paper provided by Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University in its series CAMA Working Papers with number 2008-02.

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Length: 34 pages
Date of creation: Jan 2008
Date of revision:
Handle: RePEc:een:camaaa:2008-02
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  1. George Loewenstein & Richard H Thaler, 2003. "Anomalies: Intertemporal Choice," Levine's Working Paper Archive 618897000000000784, David K. Levine.
  2. 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.
  3. Christopher Harris & David Laibson, 1999. "Dynamic Choices of Hyperbolic Consumers," Harvard Institute of Economic Research Working Papers 1886, Harvard - Institute of Economic Research.
  4. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-47, April.
  5. Partha Dasgupta & Eric Maskin, 2004. "Uncertainty and Hyperbolic Discounting," Economics Working Papers 0023, Institute for Advanced Study, School of Social Science.
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