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On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type

  • Montrucchio, Luigi
  • Privileggi, Fabio

In this paper we study the existence of bubbles for pricing equilibria in a pure exchange economy à la Lucas, with infinitely lived homogeneous agents. The model is analyzed under fairly general assumptions: no restrictions either on the stochastic process governing dividends’ distribution or on the utilities (possibly unbounded) are required. We prove that the pricing equilibrium is unique as long as the agents exhibit uniformly bounded relative risk aversion. A generic uniqueness result is also given regardless of agent’s preferences. A few ”pathological” examples of economies exhibiting pricing equilibria with bubble components are constructed. Finally, a possible relationship between our approach and the theory developed by Santos and Woodford on ambiguous bubbles is investigated. The whole discussion sheds more insight on the common belief that bubbles are a marginal phenomenon in such models.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 101 (2001)
Issue (Month): 1 (November)
Pages: 158-188

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Handle: RePEc:eee:jetheo:v:101:y:2001:i:1:p:158-188
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
  2. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-81, September.
  3. William A. Brock, 1982. "Asset Prices in a Production Economy," NBER Chapters, in: The Economics of Information and Uncertainty, pages 1-46 National Bureau of Economic Research, Inc.
  4. Magill, M. & Quinzii, M., 1993. "Icomplete Markets Over an Infinite Horizon: Long-Lived Securities and Speculative Bubbles," Papers 9321, Southern California - Department of Economics.
  5. Kandori, Michihiro, 1988. "Equivalent Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(3), pages 401-17, August.
  6. Montrucchio, Luigi & Privileggi, Fabio, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," Journal of Economic Theory, Elsevier, vol. 101(1), pages 158-188, November.
  7. Cass, David, 1972. "On capital overaccumulation in the aggregative, neoclassical model of economic growth: A complete characterization," Journal of Economic Theory, Elsevier, vol. 4(2), pages 200-223, April.
  8. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  9. Takekuma, Shin-Ichi, 1992. "Optimal Growth under Uncertainty: A Complete Characterization of Weakly Maximal Programs," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 33(2), pages 169-182, December.
  10. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  11. Brock, William A, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Wiley Blackwell, vol. 37(2), pages 275-80, April.
  12. Wilson, Charles A., 1981. "Equilibrium in dynamic models with an infinity of agents," Journal of Economic Theory, Elsevier, vol. 24(1), pages 95-111, February.
  13. Zilcha, Itzhak, 1976. "Characterization by prices of optimal programs under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 173-183, July.
  14. Gilles, Christian & LeRoy, Stephen F, 1992. "Bubbles and Charges," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(2), pages 323-39, May.
  15. Takashi Kamihigashi, 1998. "Uniqueness of asset prices in an exchange economy with unbounded utility," Economic Theory, Springer, vol. 12(1), pages 103-122.
  16. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  17. Shell, Karl, 1971. "Notes on the Economics of Infinity," Journal of Political Economy, University of Chicago Press, vol. 79(5), pages 1002-11, Sept.-Oct.
  18. Kevin X.D. Huang & Jan Werner, 1997. "Valuation bubbles and sequential bubbles," Economics Working Papers 303, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1997.
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