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Learning and excess volatility

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  • James Bullard
  • John Duffy

Abstract

We introduce adaptive learning behavior into a general equilibrium lifecycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least squares autoregressions on past data. We show that, in contrast to the perfect foresight dynamics, the dynamical system under learning possesses equilibria characterized by persistent excess volatility in returns to capital. We explore a quantitative case for these learning equilibria. We use an evolutionary search algorithm to calibrate a version of the system under learning and show that this system can generate data that matches some features of the time series data for U.S. stock returns and per capita consumption. We argue that this finding provides support for the hypothesis that the observed excess volatility of asset returns can by explained by changes in investor expectations against a background of relatively small changes in fundamental factors.

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File URL: http://research.stlouisfed.org/wp/more/1998-016
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Bibliographic Info

Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 1998-016.

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Date of creation: 1998
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Publication status: Published in Macroeconomic Dynamics, April 2001, 5(2), pp. 272-302
Handle: RePEc:fip:fedlwp:1998-016

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Keywords: Capital ; Stock - Prices;

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References

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  1. repec:cup:macdyn:v:2:y:1998:i:3:p:287-321 is not listed on IDEAS
  2. Albert Marcet & Juan P. Nicolini, 1995. "Recurrent hyperinflations and learning," Economics Working Papers 244, Department of Economics and Business, Universitat Pompeu Fabra, revised Nov 2001.
  3. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
  4. Arifovic, Jasmina & Bullard, James & Duffy, John, 1997. " The Transition from Stagnation to Growth: An Adaptive Learning Approach," Journal of Economic Growth, Springer, vol. 2(2), pages 185-209, July.
  5. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  6. Timmermann, Allan, 1996. "Excess Volatility and Predictability of Stock Prices in Autoregressive Dividend Models with Learning," Review of Economic Studies, Wiley Blackwell, vol. 63(4), pages 523-57, October.
  7. Farebrother, R W, 1980. "The Durbin-Watson Test for Serial Correlation When There Is No Intercept in the Regression," Econometrica, Econometric Society, vol. 48(6), pages 1553-63, September.
  8. Sanford J. Grossman & Robert J. Shiller, 1981. "The Determinants of the Variability of Stock Market Prices," NBER Working Papers 0564, National Bureau of Economic Research, Inc.
  9. West, Kenneth D, 1988. " Bubbles, Fads and Stock Price Volatility Tests: A Partial Evaluation," Journal of Finance, American Finance Association, vol. 43(3), pages 639-56, July.
  10. W. Brian Arthur & John H. Holland & Blake LeBaron & Richard Palmer & Paul Taylor, 1996. "Asset Pricing Under Endogenous Expectation in an Artificial Stock Market," Working Papers 96-12-093, Santa Fe Institute.
  11. 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.
  12. Campbell, John Y, 1991. "A Variance Decomposition for Stock Returns," Economic Journal, Royal Economic Society, vol. 101(405), pages 157-79, March.
  13. Campbell, John Y., 1999. "Asset prices, consumption, and the business cycle," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 19, pages 1231-1303 Elsevier.
  14. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December.
  15. Hurd, Michael D, 1989. "Mortality Risk and Bequests," Econometrica, Econometric Society, vol. 57(4), pages 779-813, July.
  16. GRANDMONT, Jean-Michel, 1997. "Expectations formation and stability of large socioeconomic systems," CORE Discussion Papers 1997088, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Hansen, G D, 1993. "The Cyclical and Secular Behaviour of the Labour Input: Comparing Efficiency Units and Hours Worked," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 71-80, Jan.-Marc.
  18. Arifovic, Jasmina, 1996. "The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economies," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 510-41, June.
  19. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September.
  20. Hommes, Cars & Sorger, Gerhard, 1998. "Consistent Expectations Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 2(03), pages 287-321, September.
  21. 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.
  22. Timmermann, Allan G, 1993. "How Learning in Financial Markets Generates Excess Volatility and Predictability in Stock Prices," The Quarterly Journal of Economics, MIT Press, vol. 108(4), pages 1135-45, November.
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