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Journal of Risk and Uncertainty

, Volume 35, Issue 2, pp 107–127 | Cite as

Whom should we believe? Aggregation of heterogeneous beliefs

  • Christian Gollier
Article

Abstract

We examine the collective risk attitude of a group with heterogeneous beliefs. We prove that the wealth-dependent probability distribution used by the representative agent is biased in favor of the beliefs of the more risk tolerant consumers. Moreover, increasing disagreement on the state probability raises the state probability of the representative agent. It implies that when most disagreements are concentrated in the tails of the distribution, the perceived collective risk is magnified. This can help to solve the equity premium puzzle. We show that the trade volume and the equity premium are positively correlated.

Keywords

Aggregation of beliefs State-dependent utility Efficient risk sharing Disagreement Asset pricing Portfolio choices 

JEL Classification

D81 D83 

References

  1. Athey, Susan C. (2002). “Monotone Comparative Statics Under Uncertainty,” Quarterly Journal of Economics 117(1), 187–223.CrossRefGoogle Scholar
  2. Abel, Andrew B. (2002). “An Exploration of the Effects of Optimism and Doubt on Asset Returns,” Journal of Economic Dynamics and Control 26, 1075–1092.CrossRefGoogle Scholar
  3. Borch, Karl. (1960). “The Safety Loading of Reinsurance Premiums,” Skandinavisk Aktuarietskrift 153–184.Google Scholar
  4. Borch, Karl. (1962). “Equilibrium in a Reinsurance Market,” Econometrica 30, 424–444.CrossRefGoogle Scholar
  5. Bossaerts, Peter, Paolo Ghirardato, Serena Guarnaschelli, and William Zame. (2007). “The Impact of Ambiguity on Prices and Allocations in Competitive Financial Markets,” Mimeo.Google Scholar
  6. Calvet, Laurent, Jean-Michel Grandmont, and Isabelle Lemaire. (2001). “Aggregation of Heterogeneous Beliefs and Asset Pricing in Complete Financial Markets,” Mimeo, Harvard University and CREST (Paris).Google Scholar
  7. Chapman, David A. and Valery Polkovnichenko. (2006). “Heterogeneity in Preferences and Asset Market Outcomes,” Mimeo, Boston College.Google Scholar
  8. Cecchetti, Stephen G., Pok-Sang Lam, and Nelson C. Mark. (2000). “Asset Pricing with Distorted Beliefs: Are Equity Returns too Good to be True?” American Economic Review 90, 787–805.CrossRefGoogle Scholar
  9. Constantinides, Georges M. (1982). “Intertemporal Asset Pricing with Heterogeneous Consumers and Without Demand Aggregation,” Journal of Business 55, 253–267.CrossRefGoogle Scholar
  10. Drèze, Jacques. (2001). “Loss Reduction and Implicit Deductibles in Medical Insurance,” CORE Discussion Paper, University of Louvain.Google Scholar
  11. Drèze, Jacques and Aldo Rustichini. (2001). “State-Dependent Utility and Decision Theory.” In Salvador Barbera, Peter Hammond, and Christian Seidl (eds), Handbook of Utility Theory 2. Dordrecht: Kluwer.Google Scholar
  12. Gajdos, Thibault, Jean-Marc Tallon, and Jean-Christophe Vergnaud. (2005). “On the Impossibility of Preference Aggregation Under Uncertainty,” Mimeo, University of Paris 1.Google Scholar
  13. Gilboa, Itzhak, Dov Samet, and David Schmeidler. (2004). “Utilitarian Aggregation of Beliefs and Tastes,” Journal of Political Economy 112, 932–938.CrossRefGoogle Scholar
  14. Gollier, Christian. (1995). “The Comparative Statics of Changes in Risk Revisited,” Journal of Economic Theory 66, 522–536.CrossRefGoogle Scholar
  15. Gollier, Christian. (2001). The Economics of Risk and Time. Cambridge: MIT Press.Google Scholar
  16. Gollier, Christian. (2003). “Who Should We Believe? Collective Risk-taking Decisions with Heterogeneous Beliefs,” Cahiers2003/0325131, http://www.toulouse.inra.fr/leerna.
  17. Hylland, Aanund and Richard Zeckhauser. (1979). “The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values,” Econometrica 47, 1321–1336.CrossRefGoogle Scholar
  18. Ingersoll, Jonathan E. (1987). Theory of Financial Decision Making. Totowa, New Jersey: Rowman and Littlefield.Google Scholar
  19. Jouini, Elyès and Clothilde Napp. (2005). “Pessimism, Riskiness, Risk Aversion and the Market Price of Risk,” Mimeo, University of Paris-Dauphine.Google Scholar
  20. Jouini, Elyès and Clothilde Napp. (2006). “Aggregation of Heterogeneous Beliefs,” Journal of Mathematical Economics 42, 752–770.CrossRefGoogle Scholar
  21. Jouini, Elyès and Clothilde Napp. (2007). “Consensus Consumer and Intertemporal Asset Pricing with Heterogeneous Beliefs,” Review of Economic Studies 74, 1–26.CrossRefGoogle Scholar
  22. Karni, Edi. (1993). “A Definition of Subjective Probabilities with State-Dependent Preferences,” Econometrica 61, 187–198.CrossRefGoogle Scholar
  23. Karni, Edi and David Schmeidler. (1993). “On the Uniqueness of Subjective Probabilities,” Economic Theory 3, 267–277.CrossRefGoogle Scholar
  24. Kimball, Miles S. (1990). “Precautionary Savings in the Small and in the Large,” Econometrica 58, 53–73.CrossRefGoogle Scholar
  25. Leland, Hayne E. (1980). “Who Should Buy Portfolio Insurance?” Journal of Finance 35, 581–596.CrossRefGoogle Scholar
  26. Lintner, John. (1969). “The Aggregation of Investor’s Diverse Judgments and Preferences in Purely Competitive Security Markets,” Journal of Financial and Quantitative Economics 4, 347–400.CrossRefGoogle Scholar
  27. Lucas, Robert E. (1978). “Asset Prices in an Exchange Economy,” Econometrica 46, 1429–1446.CrossRefGoogle Scholar
  28. Mongin, Philippe. (1995). “Consistent Bayesian Aggregation,” Journal of Economic Theory 66, 313–351.CrossRefGoogle Scholar
  29. Nau, Robert F. (1995). “Coherent Decision Analysis with Inseparable Probabilities and Utilities,” Journal of Risk and Uncertainty 10, 71–91.CrossRefGoogle Scholar
  30. Nau, Robert F. (2003). “A Generalization of Pratt–Arrow Measure to Non-Expected-Utility Preferences and Inseparable Probability and Utility,” Management Science 49, 1089–1104.CrossRefGoogle Scholar
  31. Rothschild, Michael and Joseph Stiglitz. (1970). “Increasing Risk: I. A Definition,” Journal of Economic Theory 2, 225–243.CrossRefGoogle Scholar
  32. Rothschild, Michael and Joseph Stiglitz. (1971). “Increasing Risk: II. Its Economic Consequences,” Journal of Economic Theory 3, 66–84.CrossRefGoogle Scholar
  33. Rubinstein, Mark. (1974). “An Aggregation Theorem for Securities Markets,” Journal of Financial Economics 1, 225–244.CrossRefGoogle Scholar
  34. Varian, Hal. (1985). “Divergence of Opinion in Complete Markets,” Journal of Finance 40, 309–317.CrossRefGoogle Scholar
  35. Wilson, Robert. (1968). “The Theory of Syndicates,” Econometrica 36, 113–132.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Toulouse School of Economics (LERNA, EIF and IDEI)ToulouseFrance

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