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Scenario Analysis with Recursive Utility: Dynamic Consumption Plans for Charitable Endowments

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Abstract

We determine optimal consumption paths under a series of returns scenarios for charitable endowments with distinct tastes over investment risk and inter-temporal substitution. Charities typically prefer smooth consumption paths but are investment-risk tolerant. Using a recursive, Kreps-Porteus utility function, we model the optimal disbursement from an infinitely-lived charitable trust, then, allowing a general form for the returns density, we apply stochastic dominance relations to estimate income/substitution effects whereby a change in future returns influences the current consumption rate. The elasticity of intertemporal substitution rather than risk aversion is key: optimal consumption rises or falls as the elasticity diverges from one.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 209.

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Length: 52
Date of creation: 01 Dec 2007
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Handle: RePEc:uts:rpaper:209

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Keywords: recursive utility; stochastic dominance; inter-temporal choice;

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  2. Smith, William T., 1996. "Feasibility and transversality conditions for models of portfolio choice with non-expected utility in continuous time," Economics Letters, Elsevier, vol. 53(2), pages 123-131, November.
  3. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
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  7. Kingston, Geoffrey, 1988. "Theoretical Foundations of Constant-Proportion Portfolio Insurance," Working Papers 116, University of Sydney, School of Economics.
  8. Jonathan Gruber, 2006. "A Tax-Based Estimate of the Elasticity of Intertemporal Substitution," NBER Working Papers 11945, National Bureau of Economic Research, Inc.
  9. David K. Backus & Bryan R. Routledge & Stanley E. Zin, 2005. "Exotic Preferences for Macroeconomists," NBER Chapters, in: NBER Macroeconomics Annual 2004, Volume 19, pages 319-414 National Bureau of Economic Research, Inc.
  10. Kreps, David M & Porteus, Evan L, 1979. "Dynamic Choice Theory and Dynamic Programming," Econometrica, Econometric Society, vol. 47(1), pages 91-100, January.
  11. Weil, Philippe, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, MIT Press, vol. 105(1), pages 29-42, February.
  12. Tobin, James, 1974. "What Is Permanent Endowment Income?," American Economic Review, American Economic Association, vol. 64(2), pages 427-32, May.
  13. Dybvig, Philip H, 1995. "Dusenberry's Ratcheting of Consumption: Optimal Dynamic Consumption and Investment Given Intolerance for Any Decline in Standard of Living," Review of Economic Studies, Wiley Blackwell, vol. 62(2), pages 287-313, April.
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  15. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
  16. Stephen G. Dimmock, 2012. "Background Risk and University Endowment Funds," The Review of Economics and Statistics, MIT Press, vol. 94(3), pages 789-799, August.
  17. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
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Cited by:
  1. Stephen Satchell & Susan Thorp, 2011. "Uncertain survival and time discounting: intertemporal consumption plans for family trusts," Journal of Population Economics, Springer, vol. 24(1), pages 239-266, January.

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