IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Rational and Near-Rational Bubbles Without Drift

  • Kevin J. Lansing

    (Federal Reserve Bank of San Francisco)

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: https://www.economicdynamics.org/meetpapers/2007/paper_970.pdf
Download Restriction: no

Paper provided by Society for Economic Dynamics in its series 2007 Meeting Papers with number 970.

as
in new window

Length:
Date of creation: 2007
Date of revision:
Handle: RePEc:red:sed007:970
Contact details of provider: Postal: Society for Economic Dynamics Christian Zimmermann Economic Research Federal Reserve Bank of St. Louis PO Box 442 St. Louis MO 63166-0442 USA
Fax: 1-314-444-8731
Web page: http://www.EconomicDynamics.org/society.htm
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Abel, Andrew B., 2002. "An exploration of the effects of pessimism and doubt on asset returns," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1075-1092, July.
  2. Markus K Brunnermeier, 2002. "Bubbles and Crashes," FMG Discussion Papers dp401, Financial Markets Group.
  3. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  4. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  5. 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.
  6. Stephen G. Cecchetti & Pok-sang Lam & Nelson C. Mark, 1998. "Asset Pricing with Distorted Beliefs: Are Equity Returns Too Good To Be True?," NBER Working Papers 6354, National Bureau of Economic Research, Inc.
  7. Robert J. Shiller, 1980. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," NBER Working Papers 0456, National Bureau of Economic Research, Inc.
  8. 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.
  9. Refet Gurkaynak, 2005. "Econometric Tests of Asset Price Bubbles: Taking Stock," Finance 0504008, EconWPA.
  10. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
  11. Ikeda, Shinsuke & Shibata, Akihisa, 1992. "Fundamentals-dependent bubbles in stock prices," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 143-168, October.
  12. 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.
  13. 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.
  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. Boswijk, H.P. & Hommes C.H. & Manzan, S., 2005. "Behavioral Heterogeneity in Stock Prices," CeNDEF Working Papers 05-12, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  16. 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.
  17. repec:att:wimass:9621 is not listed on IDEAS
  18. Kevin J. Lansing, 2005. "Lock-in of extrapolative expectations in an asset pricing model," Working Paper Series 2004-06, Federal Reserve Bank of San Francisco.
  19. 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.
  20. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
  21. 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.
  22. Burnside, Craig, 1998. "Solving asset pricing models with Gaussian shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 329-340, March.
  23. Robert E. Hall, 2001. "Struggling to Understand the Stock Market," American Economic Review, American Economic Association, vol. 91(2), pages 1-11, May.
  24. Simon van Norden & Huntley Schaller & ), 1995. "Speculative Behaviour, Regime-Switching, and Stock Market Crashes," Econometrics 9502003, EconWPA.
  25. Weil, Philippe, 1990. "On the Possibility of Price Decreasing Bubbles," Econometrica, Econometric Society, vol. 58(6), pages 1467-74, November.
  26. Driffill, John & Sola, Martin, 1998. "Intrinsic bubbles and regime-switching," Journal of Monetary Economics, Elsevier, vol. 42(2), pages 357-373, July.
  27. 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.
  28. 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.
  29. Robert J. Shiller, 2002. "From Efficient Market Theory to Behavioral Finance," Cowles Foundation Discussion Papers 1385, Cowles Foundation for Research in Economics, Yale University.
  30. Engsted, Tom, 2006. "Explosive bubbles in the cointegrated VAR model," Finance Research Letters, Elsevier, vol. 3(2), pages 154-162, June.
  31. 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.
  32. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
  33. Stephen F. Le Roy, 2004. "Rational Exuberance," Journal of Economic Literature, American Economic Association, vol. 42(3), pages 783-804, September.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:red:sed007:970. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christian Zimmermann)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.