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Heterogeneous Risk Attitudes in a Continuous-Time Model

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  • Chiaki Hara

    ()
    (Institute of Economic Research, Kyoto University)

Abstract

We prove that every continuous-time model in which all consumers have time-homogeneous and time-additive utility functions and share a common probabilistic belief and a common discount rate can be reduced to a static model. This result allows us to extend some of the existing results on the representative consumer and risk-sharing rules in static models to continuous-time models. We show that the equilibrium interest rate is lower and more volatile than in the standard representative consumer economy, and that the individual consumption growth rates are more dispersed than is predicted from the first-order conditions.

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Bibliographic Info

Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 609.

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Length: 31pages
Date of creation: Dec 2005
Date of revision:
Handle: RePEc:kyo:wpaper:609

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Keywords: Heterogeneity; risk attitudes; hyperbolic absolute risk aversion; representative consumer; risk-sharing rules; mutual fund theorem; Ito's Lemma; interest rates.;

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References

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  1. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative Consumer's Risk Aversion and Efficient Risk-Sharing Rules," Discussion Paper 323, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  2. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
  3. Masao Ogaki & Qiang Zhang, 2000. "Decreasing Relative Risk Aversion and Tests of Risk Sharing," Econometric Society World Congress 2000 Contributed Papers 1588, Econometric Society.
  4. Philippe Weil, 1992. "Equilibrium Asset Prices With Undiversifiable Labor Income Risk," NBER Working Papers 3975, National Bureau of Economic Research, Inc.
  5. Dumas, Bernard, 1989. "Two-Person Dynamic Equilibrium in the Capital Market," Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 157-88.
  6. Schmedders, Karl, 2007. "Two-fund separation in dynamic general equilibrium," Theoretical Economics, Econometric Society, vol. 2(2), June.
  7. Gollier, C., 1997. "Wealth Inequality and Asset Pricing," Papers 97.486, Toulouse - GREMAQ.
  8. Townsend, Robert M, 1994. "Risk and Insurance in Village India," Econometrica, Econometric Society, vol. 62(3), pages 539-91, May.
  9. Kohara, Miki & Ohtake, Fumio & Saito, Makoto, 2002. "A Test of the Full Insurance Hypothesis: The Case of Japan," Journal of the Japanese and International Economies, Elsevier, vol. 16(3), pages 335-352, September.
  10. 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.
  11. Cochrane, John H, 1991. "A Simple Test of Consumption Insurance," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 957-76, October.
  12. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
  13. Chiaki Hara & James Huang & Christoph Kuzmics, 2006. "Efficient Risk-Sharing Rules with Heterogeneous Risk Attitudes and Background Risks," KIER Working Papers 621, Kyoto University, Institute of Economic Research.
  14. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  15. Jiang, Wang, 1996. "The term structure of interest rates in a pure exchange economy with heterogeneous investors," Journal of Financial Economics, Elsevier, vol. 41(1), pages 75-110, May.
  16. Laurent Calvet & Jean-Michel Grandmont & Isabelle Lemaire, 2001. "Aggregation of Heterogenous Beliefs and Asset Pricing in Complete Financial Markets," Working Papers 2001-01, Centre de Recherche en Economie et Statistique.
  17. Basak, Suleyman & Cuoco, Domenico, 1998. "An Equilibrium Model with Restricted Stock Market Participation," Review of Financial Studies, Society for Financial Studies, vol. 11(2), pages 309-41.
  18. Mace, Barbara J, 1991. "Full Insurance in the Presence of Aggregate Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 928-56, October.
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Cited by:
  1. Hara, Chiaki, 2008. "Complete monotonicity of the representative consumer's discount factor," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1321-1331, December.
  2. Chiaki Hara, 2009. "Heterogeneous Impatience in a Continuous-Time Model," KIER Working Papers 665, Kyoto University, Institute of Economic Research.
  3. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
  4. Chiaki Hara & James Huang & Christoph Kuzmics, 2006. "Efficient Risk-Sharing Rules with Heterogeneous Risk Attitudes and Background Risks," KIER Working Papers 621, Kyoto University, Institute of Economic Research.

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