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Complete Monotonicity of the Representative Consumer's Discount Factor

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  • Hara, Chiaki

Abstract

A univariate real-valued function is said to be completely monotone if it takes positive values and alternate the signs of its higher order derivatives, starting from everywhere negative first derivatives. We prove that the representative consumer's discount factor of a continuous-time economy under uncertainty is a power function of some completely monotone function of time satisfying certain boundary conditions if and only if it may be derived from a group of consumers having constant and equal relative risk aversion, and constant and yet possibly unequal discount rates.

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Bibliographic Info

Paper provided by Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University in its series PIE/CIS Discussion Paper with number 367.

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Length: 14 p.
Date of creation: Mar 2008
Date of revision:
Handle: RePEc:hit:piecis:367

Note: "August 25, 2007" -- p. 1
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Related research

Keywords: Complete monotonicity; discount factor; discount rate; representative consumer; expected utility; time additivity; relative risk aversion; Bernstein's theorem;

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References

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  1. Ogaki, Masao & Zhang, Qiang, 2001. "Decreasing Relative Risk Aversion and Tests of Risk Sharing," Econometrica, Econometric Society, vol. 69(2), pages 515-26, March.
  2. Townsend, R.M., 1991. "Risk and Insurance in Village India," University of Chicago - Economics Research Center 91-3, Chicago - Economics Research Center.
  3. Chiaki Hara, 2005. "Heterogeneous Risk Attitudes in a Continuous-Time Model," KIER Working Papers 609, Kyoto University, Institute of Economic Research.
  4. Maurizio Mazzocco & Shiv Saini, 2012. "Testing Efficient Risk Sharing with Heterogeneous Risk Preferences," American Economic Review, American Economic Association, vol. 102(1), pages 428-68, February.
  5. Hara, Chiaki, 2008. "Heterogeneous Impatience in a Continuous-Time Model," PIE/CIS Discussion Paper 396, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  6. Christian Gollier & Richard Zeckhauser, 2005. "Aggregation of Heterogeneous Time Preferences," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 878-896, August.
  7. Barsky, Robert B, et al, 1997. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 537-79, May.
  8. Maurizio Mazzocco & Shiv Saini, 2006. "Testing Efficient Risk Sharing with Heterogeneous Risk Preferences: Semi-parametric Tests with an Application to Village Economies," 2006 Meeting Papers 108, Society for Economic Dynamics.
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Cited by:
  1. Hara, Chiaki, 2009. "Heterogeneous Impatience in a Continuous-Time Model," PIE/CIS Discussion Paper 425, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.

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