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Complete Monotonicity of the Representative Consumer's Discount Factor

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  • Chiaki Hara

    ()
    (Institute of Economic Research, Kyoto University)

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 Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 636.

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Length: 13pages
Date of creation: Jul 2007
Date of revision:
Handle: RePEc:kyo:wpaper:636

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

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  1. Hara, Chiaki, 2008. "Heterogeneous Impatience in a Continuous-Time Model," PIE/CIS Discussion Paper, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University 396, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  2. Robert M. Townsend, . "Risk and Insurance in Village India," University of Chicago - Population Research Center, Chicago - Population Research Center 91-3a, Chicago - Population Research Center.
  3. Masao Ogaki & Qiang Zhang, 2000. "Decreasing Relative Risk Aversion and Tests of Risk Sharing," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 1588, Econometric Society.
  4. Maurizio Mazzocco & Shiv Saini, 2012. "Testing Efficient Risk Sharing with Heterogeneous Risk Preferences," American Economic Review, American Economic Association, American Economic Association, vol. 102(1), pages 428-68, February.
  5. Chiaki Hara, 2005. "Heterogeneous Risk Attitudes in a Continuous-Time Model," KIER Working Papers, Kyoto University, Institute of Economic Research 609, Kyoto University, Institute of Economic Research.
  6. 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, MIT Press, vol. 112(2), pages 537-79, May.
  7. 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, Society for Economic Dynamics 108, Society for Economic Dynamics.
  8. Christian Gollier & Richard Zeckhauser, 2005. "Aggregation of Heterogeneous Time Preferences," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 113(4), pages 878-896, August.
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Cited by:
  1. Chiaki Hara, 2009. "Heterogeneous Impatience in a Continuous-Time Model," KIER Working Papers, Kyoto University, Institute of Economic Research 665, Kyoto University, Institute of Economic Research.

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