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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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  1. Andrew B. Abel, 2001. "An Exploration of the Effects of Pessimism and Doubt on Asset Returns," NBER Working Papers 8132, National Bureau of Economic Research, Inc.
  2. Robert E. Hall, 2001. "Struggling to Understand the Stock Market," American Economic Review, American Economic Association, vol. 91(2), pages 1-11, May.
  3. Bohl, Martin T. & Siklos, Pierre L., 2004. "The present value model of U.S. stock prices redux: a new testing strategy and some evidence," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 208-223, May.
  4. Peter Boswijk & Cars H. Hommes & Sebastiano Manzan, 2005. "Behavioral Heterogeneity in Stock Prices," Tinbergen Institute Discussion Papers 05-052/1, Tinbergen Institute.
  5. Pok-sang Lam & Stephen G. Cecchetti & Nelson C. Mark, 2000. "Asset Pricing with Distorted Beliefs: Are Equity Returns Too Good to Be True?," American Economic Review, American Economic Association, vol. 90(4), pages 787-805, September.
  6. Coakley, Jerry & Fuertes, Ana-Maria, 2006. "Valuation ratios and price deviations from fundamentals," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2325-2346, August.
  7. Brock, W.A. & Hommes, C.H., 1996. "Hetergeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model," Working papers 9621, Wisconsin Madison - Social Systems.
  8. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
  9. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
  10. Markus K Brunnermeier, 2002. "Bubbles and Crashes," FMG Discussion Papers dp401, Financial Markets Group.
  11. Driffill, John & Sola, Martin, 1998. "Intrinsic bubbles and regime-switching," Journal of Monetary Economics, Elsevier, vol. 42(2), pages 357-373, July.
  12. Weil, Philippe, 1990. "On the Possibility of Price Decreasing Bubbles," Econometrica, Econometric Society, vol. 58(6), pages 1467-74, November.
  13. Lansing, Kevin J., 2006. "Lock-In Of Extrapolative Expectations In An Asset Pricing Model," Macroeconomic Dynamics, Cambridge University Press, vol. 10(03), pages 317-348, June.
  14. Froot, Kenneth A & Obstfeld, Maurice, 1991. "Intrinsic Bubbles: The Case of Stock Prices," American Economic Review, American Economic Association, vol. 81(5), pages 1189-214, December.
  15. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
  16. Van Norden, S. & Schaller, H., 1996. "Speculative Behaviour, Regime-Switching and Stock Market Crashes," Working Papers 96-13, Bank of Canada.
  17. Diba, Behzad T & Grossman, Herschel I, 1988. "The Theory of Rational Bubbles in Stock Prices," Economic Journal, Royal Economic Society, vol. 98(392), pages 746-54, September.
  18. J. Bradford De Long & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, . "Noise Trader Risk in Financial Markets," J. Bradford De Long's Working Papers _124, University of California at Berkeley, Economics Department.
  19. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
  20. Refet S. G├╝rkaynak, 2005. "Econometric tests of asset price bubbles: taking stock," Finance and Economics Discussion Series 2005-04, Board of Governors of the Federal Reserve System (U.S.).
  21. Ovidiu L. Calin & Yu Chen & Thomas F. Cosimano & Alex A. Himonas, 2005. "Solving Asset Pricing Models when the Price-Dividend Function Is Analytic," Econometrica, Econometric Society, vol. 73(3), pages 961-982, 05.
  22. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-36, June.
  23. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-74, May.
  24. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  25. Engsted, Tom, 2006. "Explosive bubbles in the cointegrated VAR model," Finance Research Letters, Elsevier, vol. 3(2), pages 154-162, June.
  26. Jose A. Scheinkman & Wei Xiong, 2003. "Overconfidence and Speculative Bubbles," Journal of Political Economy, University of Chicago Press, vol. 111(6), pages 1183-1219, December.
  27. Ikeda, Shinsuke & Shibata, Akihisa, 1992. "Fundamentals-dependent bubbles in stock prices," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 143-168, October.
  28. Stephen F. Le Roy, 2004. "Rational Exuberance," Journal of Economic Literature, American Economic Association, vol. 42(3), pages 783-804, September.
  29. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-30, September.
  30. Robert J. Shiller, 2003. "From Efficient Markets Theory to Behavioral Finance," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 83-104, Winter.
  31. Koustas, Zisimos & Serletis, Apostolos, 2005. "Rational bubbles or persistent deviations from market fundamentals?," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2523-2539, October.
  32. Burnside, Craig, 1998. "Solving asset pricing models with Gaussian shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 329-340, March.
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Citations

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Cited by:
  1. 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.
  2. Branch, William A. & Evans, George W., 2013. "Bubbles, crashes and risk," Economics Letters, Elsevier, vol. 120(2), pages 254-258.
  3. Kevin J. Lansing, 2008. "Speculative growth and overreaction to technology shocks," Working Paper Series 2008-08, Federal Reserve Bank of San Francisco.
  4. George A. Waters, 2011. "Endogenous Rational Bubbles," Working Paper Series 20111003, Illinois State University, Department of Economics.
  5. Hommes, C.H. & Zhu, M., 2012. "Behavioral Learning Equilibria," CeNDEF Working Papers 12-09, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  6. Pei Kuang, 2013. "Imperfect Knowledge about Asset Prices and Credit Cycles," CDMA Working Paper Series 201303, Centre for Dynamic Macroeconomic Analysis.
  7. 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.
  8. Paolo Gelain & Kevin J. Lansing, 2013. "House prices, expectations, and time-varying fundamentals," Working Paper 2013/05, Norges Bank.
  9. 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.
  10. Pei Kuang, 2013. "Imperfect Knowledge About Asset Prices and Credit Cycles," Discussion Papers 13-02r, Department of Economics, University of Birmingham.
  11. Kevin J. Lansing, 2007. "Asset price bubbles," FRBSF Economic Letter, Federal Reserve Bank of San Francisco, issue oct26.
  12. 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.
  13. 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.
  14. repec:dgr:uvatin:2013014 is not listed on IDEAS
  15. Takashi Kamihigashi, 2010. "Recurrent Bubbles," Discussion Paper Series DP2010-27, Research Institute for Economics & Business Administration, Kobe University, revised Nov 2010.

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