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Rational and near-rational bubbles without drift

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  • Kevin J. Lansing

Abstract

This paper derives a general class of intrinsic rational bubble solutions in a standard Lucas-type asset pricing model. I show that the rational bubble component of the price-dividend ratio can evolve as a geometric random walk without drift. The volatility of bubble innovations depends exclusively on fundamentals. Starting from an arbitrarily small positive value, the rational bubble expands and contracts over time in an irregular, wholly endogenous fashion, always returning to the vicinity of the fundamental solution. I also examine a near-rational solution in which the representative agent does not construct separate forecasts for the fundamental and bubble components of the asset price. Rather, the agent constructs only a single forecast for the total asset price that is based on a geometric random walk without drift. The agent's forecast rule is parameterized to match the moments of observable data. In equilibrium, the actual law of motion for the price-dividend ratio is stationary, highly persistent, and nonlinear. The agent's forecast errors exhibit near-zero autocorrelation at all lags, making it difficult for the agent to detect a misspecification of the forecast rule. Unlike a rational bubble, the near-rational solution allows the asset price to occasionally dip below its fundamental value. Under mild risk aversion, the near-rational solution generates pronounced low-frequency swings in the price-dividend ratio, positive skewness, excess kurtosis, and time-varying volatility--all of which are present in long-run U.S. stock market data. An independent contribution of the paper is to demonstrate an approximate analytical solution for the fundamental asset price that employs a nonlinear change of variables.

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Bibliographic Info

Paper provided by Federal Reserve Bank of San Francisco in its series Working Paper Series with number 2007-10.

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Date of creation: 2007
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Handle: RePEc:fip:fedfwp:2007-10

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Keywords: Stock - Prices ; Forecasting;

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References

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Citations

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Cited by:
  1. William A. Branch & George W. Evans, 2013. "Bubbles, Crashes and Risk," CDMA Working Paper Series 201306, Centre for Dynamic Macroeconomic Analysis.
  2. Hommes, Cars & Zhu, Mei, 2014. "Behavioral learning equilibria," Journal of Economic Theory, Elsevier, vol. 150(C), pages 778-814.
  3. Kevin J. Lansing, 2007. "Asset price bubbles," FRBSF Economic Letter, Federal Reserve Bank of San Francisco, issue oct26.
  4. Cars Hommes & Mei Zhu, 2013. "Behavioral Learning Equilibria," Tinbergen Institute Discussion Papers 13-014/II, Tinbergen Institute.
  5. George W. Evans, 2011. "Comment on "Natural Expectations, Macroeconomic Dynamics, and Asset Pricing"," NBER Chapters, in: NBER Macroeconomics Annual 2011, Volume 26, pages 61-71 National Bureau of Economic Research, Inc.
  6. Kevin J. Lansing, 2008. "Speculative growth and overreaction to technology shocks," Working Paper Series 2008-08, Federal Reserve Bank of San Francisco.
  7. George A. Waters, 2011. "Endogenous Rational Bubbles," Working Paper Series 20111003, Illinois State University, Department of Economics.
  8. Paolo Gelain & Kevin J. Lansing, 2013. "House prices, expectations, and time-varying fundamentals," Working Paper 2013/05, Norges Bank.
  9. Pei Kuang, 2013. "Imperfect Knowledge about Asset Prices and Credit Cycles," Discussion Papers 13-02, Department of Economics, University of Birmingham.
  10. Airaudo, Marco & Cardani, Roberta & Lansing, Kevin J., 2013. "Monetary policy and asset prices with belief-driven fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1453-1478.
  11. Lansing, Kevin J., 2012. "Speculative growth, overreaction, and the welfare cost of technology-driven bubbles," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 461-483.
  12. Pei Kuang, 2013. "Imperfect Knowledge About Asset Prices and Credit Cycles," Discussion Papers 13-02r, Department of Economics, University of Birmingham.
  13. John Knight & Stephen Satchell & Nandini Srivastava, 2012. "Steady-State Distributions for Models of Bubbles: their Existence and Econometric Implications," Birkbeck Working Papers in Economics and Finance 1208, Birkbeck, Department of Economics, Mathematics & Statistics.
  14. Bond, Derek & Gallagher, Emer & Ramsey, Elaine, 2012. "A preliminary investigation of northern Ireland's housing market dynamics," MPRA Paper 39806, University Library of Munich, Germany.

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