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Uncertain survival and time discounting: intertemporal consumption plans for family trusts

Abstract

We derive expressions for optimal consumption for family trusts with random wealth and uncertain survival. Using UK birth statistics and the theory of branching processes, we compute size and survival probabilities for single- and multiple-branch families. Survival for a single-branch family is approximated by a Pareto distribution and consumption policies exhibit decreasing discount rates, but multiple-branch families use non-monotonic discount rates. When trust distributions depend on the number of beneficiaries rather than the survival of the whole family unit, spending paths depend on expected membership and the elasticity of intertemporal substitution. We report examples of consumption paths for a range of family trusts with constant relative risk aversion preferences.

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Notes

  1. We thank Mr. Vincent Taubman of TD Asset Management for drawing our attention to some of the legal constraints on trust deeds and trustees.

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Acknowledgements

We thank participants at the School of Economics and Finance, Queensland University of Technology, Seminar, and the Econometrics Society Australasian Meetings 2008, two anonymous referees and the editor for helpful comments. Thorp acknowledges support from ARC DP0877219.

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Correspondence to Susan Thorp.

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Responsible editor: Alessandro Cigno

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Satchell, S.E., Thorp, S. Uncertain survival and time discounting: intertemporal consumption plans for family trusts. J Popul Econ 24, 239–266 (2011). https://doi.org/10.1007/s00148-009-0297-9

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  • DOI: https://doi.org/10.1007/s00148-009-0297-9

Keywords

  • Intertemporal choice
  • Family extinction
  • Hyperbolic discounting

JEL Classification

  • G0
  • D91
  • D81