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Informational Efficiency and Endogenous Rational Bubbles

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Uncertainty, Expectations and Asset Price Dynamics

Part of the book series: Dynamic Modeling and Econometrics in Economics and Finance ((DMEF,volume 24))

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Abstract

In a model where rational bubbles form and collapse endogenously, properly specified tests of return predictability have little power to reject deviations from the efficient markets model. A weighted replicator dynamic describes how agents switch between a forecast based on fundamentals, a rational bubble forecast, and a weighted average of the two. A significant portion of the population may adopt the rational bubble forecast, which is inconsistent with the efficient markets model but satisfies informational efficiency. Tests on simulated data show excess variance in the price and unpredictable returns.

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Notes

  1. 1.

    This terminology is used by Shiller (1981). Others refer to the model as representing the strong efficient markets hypothesis.

  2. 2.

    Shiller (1981) and LeRoy and Porter (1981) show evidence of excess volatility.

  3. 3.

    Similarly, the noise trader model of DeLong et al. (1991) has deviations from the strong EMH, but the relationship to return predictability is discussed informally.

  4. 4.

    These papers are part of a large literature using the multinomial logit dynamics to describe the evolution of heterogeneous forecasts. See Hommes (2006) for a survey.

  5. 5.

    The term UA is not a covariance strictly speaking. The word is used descriptively, since the term depends on the covariances between the shocks and the level of martingale.

  6. 6.

    For model with drift, dividends would be defined as deviations from the deterministic model.

  7. 7.

    The timing for the present work is chosen to avoid complications in the tests for return predictability.

  8. 8.

    Given the timing of the present version of the model, the covariance terms may not cancel out to zero, but their impact is minimal.

  9. 9.

    A referee notes that such minima could be interpreted as arising from hedge funds with fixed strategies and the leverage to support their approach.

  10. 10.

    LeBaron et al. (1999) and Branch and Evans (2011) use stationary dividends. Adam et al. (2016) and Lansing (2010) both model dividends as a random walk with drift, which would complicate the present model and is left as a possibility for future work.

  11. 11.

    Some examples are LeRoy and Porter (1981), Campbell and Shiller (1989), and LeRoy and Parke (1992). The issue is complicated since some of these models account for a time-varying interest rate or discount factor.

  12. 12.

    For all the tests, the simulations are initialized with 50 periods followed by a run of 100, which is similar to the samples used for calibration. The table report the results over 10,000 runs.

References

  • Abou, A., & Prat, G. (2000). Modelling stock price expectations: Lessons from microdata. In F. Gardes & G. Prat (Eds.), Price expectations in goods and financial markets (pp. 313–46). Cheltenham: Edward Elgar.

    Google Scholar 

  • Adam, K., Marcet, A., & Niccolini, J. P. (2016). Stock market volatility and learning. Journal of Finance, 71, 33–82.

    Article  Google Scholar 

  • Blanchard, O. (1979). Backward and forward solutions for economies with rational expectations. American Economic Review, 69(2), 114–118.

    Google Scholar 

  • Branch, W., & Evans, G. (2007). Model uncertainty and endogenous volatility. Review of Economic Dynamics, 10, 207–237.

    Article  Google Scholar 

  • Branch, W., & Evans, G. (2011). Learning about risk and return: A simple model of bubbles and crashes. American Economic Review: Macroeconomics, 3(1), 159–191.

    Google Scholar 

  • Brock, W. A., & Hommes, C. H. (1997). A rational route to randomness. Econometrica, 65(5), 1059–1095.

    Article  Google Scholar 

  • Brock, W. A., & Hommes, C. H. (1998). Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics and Control, 22, 1235–1274.

    Article  Google Scholar 

  • Campbell, J. Y., & Shiller, R. J. (1989). The dividend-price ratio and expectations of future dividends and discount factors. Review of Financial Studies 1(3), 195–228.

    Article  Google Scholar 

  • Campbell, J. Y., & Yogo, M. (2006). Efficient tests of stock return predictability. Journal of Financial Economics, 81(1), 27–60.

    Article  Google Scholar 

  • Cochrane, J. (2008). A dog that did not bark: a defense of return predictability. Review of Financial Studies, 21(4), 1533–1575.

    Article  Google Scholar 

  • DeLong, B., Schleifer, A., Summers, L. H., & Waldmann, R. J. (1991). The survival of noise traders in financial markets. Journal of Business, 64(1), 1–20.

    Article  Google Scholar 

  • Evans, G. (1991). Pitfalls in testing for explosive bubbles in asset prices. American Economic Review, 81(4), 922–930.

    Google Scholar 

  • Evans, G., & Honkapohja, S. (2011). Learning as a rational foundation for macroeconomics and finance, Bank of Finland Research Discussion Paper No. 8/2011.

    Google Scholar 

  • Evans, G., & Ramey, G. (1992). Expectation calculation and macroeconomic dynamics. American Economics Review, 82(1), 207–224.

    Google Scholar 

  • Fama, E. F., & French, K. R. (1989). Business conditions and expected returns on stocks and bonds. Journal of Financial Economics, 25(1), 23–49.

    Article  Google Scholar 

  • Flavin, M. (1983). Excess volatility in the financial market: A reassessment of the empirical evidence. Journal of Political Economy, 91(6), 929–956.

    Article  Google Scholar 

  • Glassman, J., & Hassett, K. (1999). DOW 36,000. New York, NY: Three Rivers Press.

    Google Scholar 

  • Hofbauer, J., & Weibull, J. (1996). Evolutionary selection against dominated strategies. Journal of Economic Theory, 71, 558–573.

    Article  Google Scholar 

  • Hommes, C. H. (2001). Financial markets as nonlinear adaptive evolutionary systems. Quantitative Finance, 1, 149–167.

    Article  Google Scholar 

  • Hommes, C. H. (2006). Heterogeneous agent models in economics and finance. In L. Tesfatsion & K. I. Judd (Eds.), Handbook of computational economics. Agent-based computational economics, vol. 2. Amsterdam: Elsevier Science BV.

    Google Scholar 

  • Keynes, J. M. (1935). The general theory of employment, interest and money. New York, NY: Harcourt Brace.

    Google Scholar 

  • Lansing, K. (2010). Rational and near-rational bubbles without drift. Economic Journal, 120, 1149–1174.

    Article  Google Scholar 

  • LeBaron, B. (2012). Heterogeneous gain learning and the dynamics of asset prices. Journal of Economic Behavior and Organization, 83(3), 424–445.

    Article  Google Scholar 

  • LeBaron, B., Arthur, B., & Palmer, R. (1999). Time series properties of an artificial stock market. Journal of Economic Dynamics and Control, 23, 1487–1516.

    Article  Google Scholar 

  • LeRoy, S. F., & Parke, W. R. (1992). Stock price volatility: Tests based on the geometric random walk. American Economic Review, 82(4), 981–992.

    Google Scholar 

  • LeRoy, S. F., & Porter, R. D. (1981). The present value relation: Tests based on implied variance bounds. Econometrica, 49(3), 555–574.

    Article  Google Scholar 

  • Lewellen, J. (2004). Predicting returns with financial ratios. Journal of Financial Economics, 74(1), 209–235.

    Article  Google Scholar 

  • Lundqvist, L., & Sargent, T. J. (2004). Recursive macroeconomics theory. Cambridge, MA: The MIT Press.

    Google Scholar 

  • Ohlson, J. A. (1977). Risk-aversion and the martingale property of stock prices: Comments. International Economic Review, 18(1), 229–235.

    Article  Google Scholar 

  • Parke, W. R., & Waters, G. A. (2007). An evolutionary game theory explanation of arch effects. Journal of Economic Dynamics and Control, 31(7), 2234–2262.

    Article  Google Scholar 

  • Parke, W. R., & Waters, G. A. (2014). On the evolutionary stability of rational expectations. Macroeconomic Dynamics, 18(7), 1581–1606.

    Article  Google Scholar 

  • Prat, G., & Uctum, R. (2011). Modelling oil price expectations: Evidence from survey data. The Quarterly Review of Economics and Finance, 51(3), 236–247.

    Article  Google Scholar 

  • Prat G., & Uctum, R. (2015). Expectation formation in the foreign exchange market : A time-varying heterogeneity approach using survey data. Applied Economics, 47(34–35), 3673–95.

    Article  Google Scholar 

  • Samuelson, L. (1997). Evolutionary games and equilibrium selection. Cambridge, MA: The MIT Press.

    Google Scholar 

  • Sandholm, W. (2011). Population games and evolutionary dynamics. Cambridge, MA: The MIT Press.

    Google Scholar 

  • Shiller, R. J. (1981). Do stock prices move too much to be justified to expected changes in dividends? American Economics Review, 71(3), 421–426.

    Google Scholar 

  • Shiller, R. J. (1990). The term structure of interest rates. In B. M. Friedman & F. H. Hahn (Eds.), The handbook of monetary economics. Amsterdam: Elsevier Science BV.

    Google Scholar 

  • Shiller, R. J. (2005). Irrational exuberance. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Waters, G. A. (2009). Chaos in the cobweb model with a new learning dynamic. Journal of Economic Dynamics and Control, 33(6), 1201–1216.

    Article  Google Scholar 

  • Weibull, J. (1998). Evolutionary game theory. Cambridge, MA: MIT Press.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Economics, Illinois State University, Normal, IL, USA

    George A. Waters

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  1. George A. Waters
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Editors and Affiliations

  1. Lille University, Lille Cedex, France

    Fredj Jawadi

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Waters, G.A. (2018). Informational Efficiency and Endogenous Rational Bubbles. In: Jawadi, F. (eds) Uncertainty, Expectations and Asset Price Dynamics. Dynamic Modeling and Econometrics in Economics and Finance, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-98714-9_7

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